Bridget Nkemnole | University of Lagos (original) (raw)

Papers by Bridget Nkemnole

JSTA, 2020

This paper proposes a weighting of the exponentiated gamma distribution with a polynomial functio... more This paper proposes a weighting of the exponentiated gamma distribution with a polynomial function called the poly-weighted exponentiated gamma distribution (PWEGD). It shows that the modified distribution harnesses the multi-dimensional effects of the distribution. We provided an extensive mathematical treatment of this proposed distribution: obtained its parameters, estimated its statistical properties with applicable, tests and compared the estimates with existing distribution. The study estimated the cumulative distribution function, hazard function, survival function, skewness, kurtosis, mode, median and quar-tiles of the distribution and evaluated the distribution with Monte Carlo simulated data and the data of the wind direction (degrees) in Lagos, Nigeria. Empirical analysis showed that with increased polynomial function, the estimates and the statistical properties like the expectation, variance, standard error, median, mode, hazard and survival functions, cumulative distribution function (CDF), moments, skewness and kurtosis were significantly better than the existing root distributions. The MSE of the parameters decreased with increased power and the parameter is significant (p <0.05). It is concluded that the proposed distribution does not only provide better fitting but also establishes an efficient structure for lifetime data modelling.

DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2021

Journal of Modern Applied Statistical Methods, 2013

A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model... more A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model (HMM). The SV model assumes that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes the SV model with the student-t distribution and the generalized error distribution (GED) and compares these distributions with a mixture of normal distributions from Kim and Stoffer (2008). A Sequential Monte Carlo with Expectation Maximization (SMCEM) algorithm technique was used to estimate parameters for the extended volatility model; the Akaike Information Criteria (AIC) and forecast statistics were calculated to compare distribution fit. Distribution performance was assessed using simulation study and real data. Results show that, although comparable to the normal mixture SV model, the Student-t and GED were empirically more successful.

Journal of the Nigerian Mathematical Society, 2015

Stochastic Volatility (SV) model usually assumes that the distribution of asset returns condition... more Stochastic Volatility (SV) model usually assumes that the distribution of asset returns conditional on the latent volatility is normal. Previous approaches to estimation of SV model have mostly focused on Gaussian filters in practice. This paper analyzes SV model with the student-t distribution and compares the distribution with mixture-of-normal distributions of Kim and Stoffer [22]. A Sequential Monte Carlo with Expectation-Maximization (SMCEM) technique based on student-t distribution is developed to estimate the parameters for the extended volatility model. The SMC method, or particle filter based on student-t distribution, which is heavier tailed than Gaussians, provides an approximate solution to non-Gaussian estimation problem and hence more robust. Our empirical analysis indicates that extension of the SV model such as a specification of the error term with student-t distribution in the return equation dominates the normal mixture distribution. Additionally, the t-distribution based particle filter is applied to a multivariate stochastic volatility model. It is again shown that the student-t based algorithm performs quite well in explaining the joint dynamics in the volatility of a set of four exchange rates series. c

The use of volatility models to generate volatility forecasts has given vent to a lot of literatu... more The use of volatility models to generate volatility forecasts has given vent to a lot of literature. However, it is known that volatility persistence, as indicated by the estimated parameter rp , in Stochastic Volatility (SV) model is typically high. Since future values in SV models are based on the estimation of the parameters, this may lead to poor volatility forecasts. Furthermore. this high persistence, as contended by some writers, is due 10 the structure changes (e.g. shift of volatility levels) in the volatility processes, which SV model cannot capture. This work deals with the problem by bringing in the SV model based on Hidden Markov Models (HMMs), called HMM-SV model. Via hidden states, HMMs allow for periods 'with different volatility levels characterized by the hidden states. Within each state, SV model is applied to model conditional volatility. Empirical analysis shows that our model, not only takes care of the structure changes (hence giving better volatility fore...

Journal of Applied Sciences and Environmental Management

This study tends to examine the push-pull model on the effect of covid-19 on the employment stabi... more This study tends to examine the push-pull model on the effect of covid-19 on the employment stability in the private and informal sector in parts of Lagos state, Nigeria. Survey method was adopted and population was drawn from employees across the low income private and informal sector in some of the LGA of Lagos state, Nigeria. Questionnaire was sent through the Google form via e-mails and WhatsApp to about 245 target respondents and 229 was returned completed. A Push-Pull model was developed using stochastic statistical model to obtain the transition probabilities and the stationary distribution. The results revealed that 132, with transitional probability of 0.5788, of low-income private sector employees remain on the job and are willing to pull back to work while 92 individuals with transitional probability of 0.4057 wish to explore other industries and only 5 employees with transitional probability of 0.0165 were ready to defect to other industry.

Journal of Applied Sciences and Environmental Management

The study considered the birth gap with four states, length of breastfeeding with four states and... more The study considered the birth gap with four states, length of breastfeeding with four states and type of contraceptives used with five states, by mothers with at least three conceptions in Lagos Metropolis, Nigeria. Data was obtained from the population using a self-designed and administered questionnaire. Results showed that the steady state probability of birth gap was highest at state 4 which is > 24 months implying that 3 out of five women on the long – run will space their births at more than 2 years which ultimately will lead to lower child birth, improved mother’s welfare and healthier children. Also, the distribution of mothers and their switching after each period of childbirth shows that contraceptives are indeed effective in controlling conception. Lastly, the transition probabilities of the states are significantly greater than zero and the state are dependent on each other (p < 0.05). The study therefore concluded that increased birth gaps, elongated length of br...

Journal of Statistics Applications & Probability, 2016

This research investigates the endemic level and (knowledg e of) persistence time of endemic dise... more This research investigates the endemic level and (knowledg e of) persistence time of endemic diseases in a population us ng a Stochastic Model such as Markov process which is a continuou s time and discrete state space that requires the Monte Carlo Simulation for the desired results to be gotten. It assesses some areas o f active research in efficient procedures for simulation in h ealth sector and addresses the influence of gender as regards to the average da ys a p rticular disease dies out. There is also an emphasis on the average population to be infected on a monthly basis. The data used fo r this study is obtained from the medical records that runs fr om January 2012 through December 2012 of General Hospital Gbagada, Lag os State which comprises of children from ages 0 to 12years an d adults from ages 13years and above. The Monte Carlo simulation carr ied out shows the trend line and equations of the data. Empiri cal analysis showed a significant relationship between gender and persis t nce time of endemic diseases in a population.

Theoretical and Applied Economics, 2017

The use of volatility models to conduct volatility forecasting is gaining momentum in empirical l... more The use of volatility models to conduct volatility forecasting is gaining momentum in empirical literature. The performance of volatility persistence, as indicated by the estimated parameter φ, in Stochastic Volatility (SV) model is typically high. Since future values in SV models are based on the estimation of the parameters, this may lead to poor volatility forecasts. Furthermore, this high persistence, according to some research scientists, is due to the structure changes (e.g. shift of volatility levels) in the volatility processes, which SV model cannot capture. Hidden Markov Models (HMMs) allow for periods with different volatility levels characterized by the hidden states. This work deals with the problem by bringing in the SV model based on Hidden Markov Models (HMMs), called HMM-SV model. Via hidden states, HMMs allow for periods with different volatility levels characterized by the hidden states. Within each state, SV model is applied to model conditional volatility. Empir...

The constant concern in commodities market, particularly in oil price, has necessitated accurate ... more The constant concern in commodities market, particularly in oil price, has necessitated accurate models to aid in the generation of relatively good synthetic oil price data. Oil prices are subject to high volatility and its impact on economic growth has continued to generate controversies among economic researchers and policymakers. In this paper, a state space model approach was developed to describe the dynamics of Brent crude oil prices. The dynamics were examined as a continuous time stochastic process generalized as an Ornstein-Uhlenbeck equation. The result revealed that the dynamic behaviour of Brent oil price is an Ornstein-Uhlenbeck equation depicting a mean reversion process in crude oil prices. The process is stationary Gauss-Markov process and is the only nontrivial process that satisfies the conditions of allowing linear transformations of the space and time variables. The Ornstein-Uhlenbeck process in this paper is considered as the continuous time analogue of the disc...

Bearings-only target tracking is a nonlinear estimation problem often addressed by linearised fil... more Bearings-only target tracking is a nonlinear estimation problem often addressed by linearised filters where the uncertainty in the sensor and motion models is typically modeled by Gaussian densities. In this paper, a particle filter or sequential Monte Carlo method is developed, based on student-t distribution, which is heavier tailed than Gaussian’s and hence more robust. The t-distribution-based particle filter provides an approximate solution to nonlinear non-Gaussian estimation problems. To estimate the target state based on samples, an expectation maximisation (EM)-type algorithm was developed and embedded in a student-t particle filter. The expectation step was implemented by the particle filter. In this step, the distribution of the states and the state vector were estimated. Consequently, in the maximisation step, the nonlinear observation equation was approximated as a mixture of the Gaussian and student-t models. A bearings-only tracking problem was simulated to present th...

The Markov switching GARCH model offers rich dynamics to modelling financial data. Estimating thi... more The Markov switching GARCH model offers rich dynamics to modelling financial data. Estimating this path dependence model is a challenging task because exact computation of the likelihood is impracticable in real life. This has led to so many numerical computational methods to obtain the maximum likelihood. Just as so many numerical methods have been adopted to estimate the likelihood function, others have also adopted other methods of estimation to model this path dependence model. In this research work, the method of maximum likelihood (ML) and the Bayesian method (BM) of estimation were used in estimating the parameters of the Markov-switching GARCH model for single regime, two regime and three regime and was applied to exchange rate data. It was discovered that the three regime switching GARCH model outperformed the other regime switching model for the method of ML based on their information criteria and the two regime switching performed better based on the deviance information ...

International Journal of Probability and Statistics, 2014

Target tracking is the problem of generating an inference engine on the state of a target using a... more Target tracking is the problem of generating an inference engine on the state of a target using a sequence of observations in time, which is to recursively estimate the probability density function of the target state. Traditionally, linearized models are used, where the uncertainty in the sensor and motion models is typically modeled by Gaussian densities. In this paper, the sequential Monte Carlo (SMC) method is developed based on Student's-t distribution, which is heavier tailed than Gaussians and hence more robust, The SMC method, or particle filter, provides an approximate solution to non-Gaussian estimation problem. To estimate the target state based on samples, an EM-type algorithm is developed and embedded in the Student's-t particle filter. The expectation (E) step is implemented by the particle filter. Within this step, the distribution of the states given the observations, and the state vector are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians model and the Student's-t model. A bearings-only tracking (BOT) problem is simulated to present the implementation of the particle filter algorithm based on both the mixture of Gaussians model and the Student's-t. Simulations have demonstrated the effectiveness and the improved performance of the Student's-t based particle filter over Gaussians mixture model. Additionally, the method is applied to real life data taken from the digital GSM real-time data logging tracking system. It is again shown that the Student's-t based algorithm is successful in accommodating nonlinear model for a target tracking scenario.

The combination of Shewhart X and S-control charts developed to control the process variability b... more The combination of Shewhart X and S-control charts developed to control the process variability based on the assumption that the underlying distribution of the quality characteristic is normal. The normality assumption is often violated when the underlying distribution of the characteristic under consideration is skewed; therefore, the use of the Shewhart X and S control charts on real-life data might lead to inaccurate estimation of control limits. The robust methods of estimation of control chart statistics can be used in such situations. In this paper, the robust scale estimator was used to estimate the mean, variance and median based on Marshall-Olkin Inverse log-logistic distribution. Monte Carlo simulation study was conducted using Marshall-Olkin Inverse log-logistic distribution to determine the performance of the proposed method in comparison with the Shewhart S and MAD methods. The proposed control limits showed an improvement over the Shewhart and stocktickerMAD control ch...

African Journal of Pure and Applied Sciences, 2020

The fundamental assumption of variable control charts is that the data are normally distributed a... more The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Di...

Journal of Economic and Financial Sciences, 2016

The movement of stock prices, in capital markets across the world, has been found to be both rand... more The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and t...

American Journal of Business Education (AJBE), 2010

The study compares the performance of distance learning students with full-time students in a tra... more The study compares the performance of distance learning students with full-time students in a traditional face-to-face learning environment. This study is one aspect of a larger research project designed to gain insight into factors that may influence the performance of distance learning students. The data used in the study represent the graduating GPA (Grade Point Average) and CGPA (Cumulative Grade Point Average). The result showed that students of Distance Learning Institute (DLI) performed better in business administration than the mainstream students, while the mainstream accounting students perform better than the DLI accounting students. Results indicated that there was a statistically significant difference in final grades of these groups of students.

Journal of Statistical Theory and Applications, 2020

Journal of Economic and Financial Sciences, 2019

Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of... more Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, such as heavy tails and excess kurtosis.Research purpose: This work was aimed at analysing the GBM with a sequential Monte Carlo (SMC) technique based on t-distribution and compares the distribution with normal distribution.Motivation for the study: The SMC or particle filter based on the t-distribution for the GBM model, which involves randomness, volatility and drift, can precisely capture the aforementioned statistical characteristics of return distributions and can predict the random changes or fluctuation in stock prices.Research approach/design and method: The particle filter based on the t-distribution is developed to estimate the random effects and parameters for the extended model...

JSTA, 2020

This paper proposes a weighting of the exponentiated gamma distribution with a polynomial functio... more This paper proposes a weighting of the exponentiated gamma distribution with a polynomial function called the poly-weighted exponentiated gamma distribution (PWEGD). It shows that the modified distribution harnesses the multi-dimensional effects of the distribution. We provided an extensive mathematical treatment of this proposed distribution: obtained its parameters, estimated its statistical properties with applicable, tests and compared the estimates with existing distribution. The study estimated the cumulative distribution function, hazard function, survival function, skewness, kurtosis, mode, median and quar-tiles of the distribution and evaluated the distribution with Monte Carlo simulated data and the data of the wind direction (degrees) in Lagos, Nigeria. Empirical analysis showed that with increased polynomial function, the estimates and the statistical properties like the expectation, variance, standard error, median, mode, hazard and survival functions, cumulative distribution function (CDF), moments, skewness and kurtosis were significantly better than the existing root distributions. The MSE of the parameters decreased with increased power and the parameter is significant (p <0.05). It is concluded that the proposed distribution does not only provide better fitting but also establishes an efficient structure for lifetime data modelling.

DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2021

Journal of Modern Applied Statistical Methods, 2013

A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model... more A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model (HMM). The SV model assumes that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes the SV model with the student-t distribution and the generalized error distribution (GED) and compares these distributions with a mixture of normal distributions from Kim and Stoffer (2008). A Sequential Monte Carlo with Expectation Maximization (SMCEM) algorithm technique was used to estimate parameters for the extended volatility model; the Akaike Information Criteria (AIC) and forecast statistics were calculated to compare distribution fit. Distribution performance was assessed using simulation study and real data. Results show that, although comparable to the normal mixture SV model, the Student-t and GED were empirically more successful.

Journal of the Nigerian Mathematical Society, 2015

Stochastic Volatility (SV) model usually assumes that the distribution of asset returns condition... more Stochastic Volatility (SV) model usually assumes that the distribution of asset returns conditional on the latent volatility is normal. Previous approaches to estimation of SV model have mostly focused on Gaussian filters in practice. This paper analyzes SV model with the student-t distribution and compares the distribution with mixture-of-normal distributions of Kim and Stoffer [22]. A Sequential Monte Carlo with Expectation-Maximization (SMCEM) technique based on student-t distribution is developed to estimate the parameters for the extended volatility model. The SMC method, or particle filter based on student-t distribution, which is heavier tailed than Gaussians, provides an approximate solution to non-Gaussian estimation problem and hence more robust. Our empirical analysis indicates that extension of the SV model such as a specification of the error term with student-t distribution in the return equation dominates the normal mixture distribution. Additionally, the t-distribution based particle filter is applied to a multivariate stochastic volatility model. It is again shown that the student-t based algorithm performs quite well in explaining the joint dynamics in the volatility of a set of four exchange rates series. c

The use of volatility models to generate volatility forecasts has given vent to a lot of literatu... more The use of volatility models to generate volatility forecasts has given vent to a lot of literature. However, it is known that volatility persistence, as indicated by the estimated parameter rp , in Stochastic Volatility (SV) model is typically high. Since future values in SV models are based on the estimation of the parameters, this may lead to poor volatility forecasts. Furthermore. this high persistence, as contended by some writers, is due 10 the structure changes (e.g. shift of volatility levels) in the volatility processes, which SV model cannot capture. This work deals with the problem by bringing in the SV model based on Hidden Markov Models (HMMs), called HMM-SV model. Via hidden states, HMMs allow for periods 'with different volatility levels characterized by the hidden states. Within each state, SV model is applied to model conditional volatility. Empirical analysis shows that our model, not only takes care of the structure changes (hence giving better volatility fore...

Journal of Applied Sciences and Environmental Management

This study tends to examine the push-pull model on the effect of covid-19 on the employment stabi... more This study tends to examine the push-pull model on the effect of covid-19 on the employment stability in the private and informal sector in parts of Lagos state, Nigeria. Survey method was adopted and population was drawn from employees across the low income private and informal sector in some of the LGA of Lagos state, Nigeria. Questionnaire was sent through the Google form via e-mails and WhatsApp to about 245 target respondents and 229 was returned completed. A Push-Pull model was developed using stochastic statistical model to obtain the transition probabilities and the stationary distribution. The results revealed that 132, with transitional probability of 0.5788, of low-income private sector employees remain on the job and are willing to pull back to work while 92 individuals with transitional probability of 0.4057 wish to explore other industries and only 5 employees with transitional probability of 0.0165 were ready to defect to other industry.

Journal of Applied Sciences and Environmental Management

The study considered the birth gap with four states, length of breastfeeding with four states and... more The study considered the birth gap with four states, length of breastfeeding with four states and type of contraceptives used with five states, by mothers with at least three conceptions in Lagos Metropolis, Nigeria. Data was obtained from the population using a self-designed and administered questionnaire. Results showed that the steady state probability of birth gap was highest at state 4 which is > 24 months implying that 3 out of five women on the long – run will space their births at more than 2 years which ultimately will lead to lower child birth, improved mother’s welfare and healthier children. Also, the distribution of mothers and their switching after each period of childbirth shows that contraceptives are indeed effective in controlling conception. Lastly, the transition probabilities of the states are significantly greater than zero and the state are dependent on each other (p < 0.05). The study therefore concluded that increased birth gaps, elongated length of br...

Journal of Statistics Applications & Probability, 2016

This research investigates the endemic level and (knowledg e of) persistence time of endemic dise... more This research investigates the endemic level and (knowledg e of) persistence time of endemic diseases in a population us ng a Stochastic Model such as Markov process which is a continuou s time and discrete state space that requires the Monte Carlo Simulation for the desired results to be gotten. It assesses some areas o f active research in efficient procedures for simulation in h ealth sector and addresses the influence of gender as regards to the average da ys a p rticular disease dies out. There is also an emphasis on the average population to be infected on a monthly basis. The data used fo r this study is obtained from the medical records that runs fr om January 2012 through December 2012 of General Hospital Gbagada, Lag os State which comprises of children from ages 0 to 12years an d adults from ages 13years and above. The Monte Carlo simulation carr ied out shows the trend line and equations of the data. Empiri cal analysis showed a significant relationship between gender and persis t nce time of endemic diseases in a population.

Theoretical and Applied Economics, 2017

The use of volatility models to conduct volatility forecasting is gaining momentum in empirical l... more The use of volatility models to conduct volatility forecasting is gaining momentum in empirical literature. The performance of volatility persistence, as indicated by the estimated parameter φ, in Stochastic Volatility (SV) model is typically high. Since future values in SV models are based on the estimation of the parameters, this may lead to poor volatility forecasts. Furthermore, this high persistence, according to some research scientists, is due to the structure changes (e.g. shift of volatility levels) in the volatility processes, which SV model cannot capture. Hidden Markov Models (HMMs) allow for periods with different volatility levels characterized by the hidden states. This work deals with the problem by bringing in the SV model based on Hidden Markov Models (HMMs), called HMM-SV model. Via hidden states, HMMs allow for periods with different volatility levels characterized by the hidden states. Within each state, SV model is applied to model conditional volatility. Empir...

The constant concern in commodities market, particularly in oil price, has necessitated accurate ... more The constant concern in commodities market, particularly in oil price, has necessitated accurate models to aid in the generation of relatively good synthetic oil price data. Oil prices are subject to high volatility and its impact on economic growth has continued to generate controversies among economic researchers and policymakers. In this paper, a state space model approach was developed to describe the dynamics of Brent crude oil prices. The dynamics were examined as a continuous time stochastic process generalized as an Ornstein-Uhlenbeck equation. The result revealed that the dynamic behaviour of Brent oil price is an Ornstein-Uhlenbeck equation depicting a mean reversion process in crude oil prices. The process is stationary Gauss-Markov process and is the only nontrivial process that satisfies the conditions of allowing linear transformations of the space and time variables. The Ornstein-Uhlenbeck process in this paper is considered as the continuous time analogue of the disc...

Bearings-only target tracking is a nonlinear estimation problem often addressed by linearised fil... more Bearings-only target tracking is a nonlinear estimation problem often addressed by linearised filters where the uncertainty in the sensor and motion models is typically modeled by Gaussian densities. In this paper, a particle filter or sequential Monte Carlo method is developed, based on student-t distribution, which is heavier tailed than Gaussian’s and hence more robust. The t-distribution-based particle filter provides an approximate solution to nonlinear non-Gaussian estimation problems. To estimate the target state based on samples, an expectation maximisation (EM)-type algorithm was developed and embedded in a student-t particle filter. The expectation step was implemented by the particle filter. In this step, the distribution of the states and the state vector were estimated. Consequently, in the maximisation step, the nonlinear observation equation was approximated as a mixture of the Gaussian and student-t models. A bearings-only tracking problem was simulated to present th...

The Markov switching GARCH model offers rich dynamics to modelling financial data. Estimating thi... more The Markov switching GARCH model offers rich dynamics to modelling financial data. Estimating this path dependence model is a challenging task because exact computation of the likelihood is impracticable in real life. This has led to so many numerical computational methods to obtain the maximum likelihood. Just as so many numerical methods have been adopted to estimate the likelihood function, others have also adopted other methods of estimation to model this path dependence model. In this research work, the method of maximum likelihood (ML) and the Bayesian method (BM) of estimation were used in estimating the parameters of the Markov-switching GARCH model for single regime, two regime and three regime and was applied to exchange rate data. It was discovered that the three regime switching GARCH model outperformed the other regime switching model for the method of ML based on their information criteria and the two regime switching performed better based on the deviance information ...

International Journal of Probability and Statistics, 2014

Target tracking is the problem of generating an inference engine on the state of a target using a... more Target tracking is the problem of generating an inference engine on the state of a target using a sequence of observations in time, which is to recursively estimate the probability density function of the target state. Traditionally, linearized models are used, where the uncertainty in the sensor and motion models is typically modeled by Gaussian densities. In this paper, the sequential Monte Carlo (SMC) method is developed based on Student's-t distribution, which is heavier tailed than Gaussians and hence more robust, The SMC method, or particle filter, provides an approximate solution to non-Gaussian estimation problem. To estimate the target state based on samples, an EM-type algorithm is developed and embedded in the Student's-t particle filter. The expectation (E) step is implemented by the particle filter. Within this step, the distribution of the states given the observations, and the state vector are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians model and the Student's-t model. A bearings-only tracking (BOT) problem is simulated to present the implementation of the particle filter algorithm based on both the mixture of Gaussians model and the Student's-t. Simulations have demonstrated the effectiveness and the improved performance of the Student's-t based particle filter over Gaussians mixture model. Additionally, the method is applied to real life data taken from the digital GSM real-time data logging tracking system. It is again shown that the Student's-t based algorithm is successful in accommodating nonlinear model for a target tracking scenario.

The combination of Shewhart X and S-control charts developed to control the process variability b... more The combination of Shewhart X and S-control charts developed to control the process variability based on the assumption that the underlying distribution of the quality characteristic is normal. The normality assumption is often violated when the underlying distribution of the characteristic under consideration is skewed; therefore, the use of the Shewhart X and S control charts on real-life data might lead to inaccurate estimation of control limits. The robust methods of estimation of control chart statistics can be used in such situations. In this paper, the robust scale estimator was used to estimate the mean, variance and median based on Marshall-Olkin Inverse log-logistic distribution. Monte Carlo simulation study was conducted using Marshall-Olkin Inverse log-logistic distribution to determine the performance of the proposed method in comparison with the Shewhart S and MAD methods. The proposed control limits showed an improvement over the Shewhart and stocktickerMAD control ch...

African Journal of Pure and Applied Sciences, 2020

The fundamental assumption of variable control charts is that the data are normally distributed a... more The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Di...

Journal of Economic and Financial Sciences, 2016

The movement of stock prices, in capital markets across the world, has been found to be both rand... more The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and t...

American Journal of Business Education (AJBE), 2010

The study compares the performance of distance learning students with full-time students in a tra... more The study compares the performance of distance learning students with full-time students in a traditional face-to-face learning environment. This study is one aspect of a larger research project designed to gain insight into factors that may influence the performance of distance learning students. The data used in the study represent the graduating GPA (Grade Point Average) and CGPA (Cumulative Grade Point Average). The result showed that students of Distance Learning Institute (DLI) performed better in business administration than the mainstream students, while the mainstream accounting students perform better than the DLI accounting students. Results indicated that there was a statistically significant difference in final grades of these groups of students.

Journal of Statistical Theory and Applications, 2020

Journal of Economic and Financial Sciences, 2019

Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of... more Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, such as heavy tails and excess kurtosis.Research purpose: This work was aimed at analysing the GBM with a sequential Monte Carlo (SMC) technique based on t-distribution and compares the distribution with normal distribution.Motivation for the study: The SMC or particle filter based on the t-distribution for the GBM model, which involves randomness, volatility and drift, can precisely capture the aforementioned statistical characteristics of return distributions and can predict the random changes or fluctuation in stock prices.Research approach/design and method: The particle filter based on the t-distribution is developed to estimate the random effects and parameters for the extended model...