Mathematical Statistics Research Papers - Academia.edu (original) (raw)

Based on the our October paper "A Generalized Viral Infection Mathematical Model Derived from Covid-19 Simulation", at a conceptual level higher than the classic SIR/SEIR model, we have established the 6 laws of infection regarding the... more

Based on the our October paper "A Generalized Viral Infection Mathematical Model Derived from Covid-19 Simulation", at a conceptual level higher than the classic SIR/SEIR model, we have established the 6 laws of infection regarding the final infection ratio within any given population without any artificial intervention and have shown the final infection ratio in a natural, non-interfered pandemic must fall within a specified lower and upper bound as 1 − 1 R 2 0 ≤ F R ≤ 2 (1 − 1 R 0). Whereas R 0 is the intrinsic R 0 value of the disease. In this paper, we show how human intervention strategies alter the previous assumptions based on 2 factors. First, artificial intervention with cycles of restricting measures and relaxations. Based on our May paper "The Predictions on Worldwide Covid-19 Pandemic Cases Based on Historical Data", we have already demonstrated the dynamic falling R 0 (t) curve during lock down measures. With more historical data and observation, we now expand the scope to include a dynamic rising R 0 (t) curve following the relaxation of measures, completing the cycle of restriction and relaxation. Second, the introduction of vaccination at a steady rate introduced a new variable into the existing infection model, we denote it as function V (t). We demonstrate the optimal strategies of vaccination interpreted within our existing established framework.

In their smash hit MATHEMATICAL STATISTICS WITH APPLICATIONS, debut creators Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a strong establishment in factual hypothesis while passing on the pertinence and... more

In their smash hit MATHEMATICAL STATISTICS WITH APPLICATIONS, debut creators Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a strong establishment in factual hypothesis while passing on the pertinence and significance of the hypothesis in taking care of viable issues in reality. The creators' utilization of pragmatic applications and fantastic activities encourages you find the idea of insights and comprehend its basic job in logical research.

We present consequential mistakes in uses of correlation in social science research, particularly psychology

Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax... more

Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax distribution based on complete data. The maximum likelihood, moment and uniformly minimum variance unbiased estimators are obtained as non-Bayes estimators. Bayes and empirical Bayes estimators are obtained corresponding to three informative priors "gamma, chi-square and inverted Levy" based on symmetric "squared error" and asymmetric "LINEX and general entropy" loss functions. The estimates of the shape parameter were compared empirically via Monte Carlo simulation study based upon the mean squared error. Among the set of conclusions that have been reached, it is observed that, for all sample sizes and different cases, the performance of uniformly minimum variance unbiased estimator is better than other non-Bayes estimators. Fur...

A method for computing Mackey-Glass equation of the form   () (), () y t f y t y t    is examined in this paper. For a given lag  , uniformly generated and fixed beta is observed for estimating the y  (density  time-units in the... more

A method for computing Mackey-Glass equation of the form   () (), () y t f y t y t    is examined in this paper. For a given lag  , uniformly generated and fixed beta is observed for estimating the y  (density  time-units in the past). The technique was applied to blood destruction and production in human body.

There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don't get the actual response. Randomized response technique (RRT) models are developed to reduce the... more

There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don't get the actual response. Randomized response technique (RRT) models are developed to reduce the bias raised by an evasive response on the sensitive variable. The measurement error (ME) is usually always present in the surveys so we need to study the RRT models with ME. We propose an estimator to predict the population mean of a sensitive variable in the influence of ME. The properties of the proposed estimator are studied and comparisons are made with the existing estimators. At last, a simulation study is executed to illustrate the results numerically.

We study asymptotically optimal statistical inference concerning the unknown state of N identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather... more

We study asymptotically optimal statistical inference concerning the unknown state of N identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up... more

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the
field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is
a three-dimensional phenomenon.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the... more

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

In this book an extension of the Weibull distribution which involves an additional shape parameter is being proposed. Interestingly, the additional parameter acts somewhat as a location parameter while the support of the distribution... more

In this book an extension of the Weibull distribution which involves an additional shape parameter is being proposed. Interestingly, the additional parameter acts somewhat as a location parameter while the support of the distribution remains the positive half-line. Since the gamma distribution
is a particular case of this distribution, the latter is referred to as a gammaWeibull distribution. Numerous distributions
such as the Rayleigh, half-normal and Maxwell distributions
can also be obtained as special cases. The moment generating function of a gamma-Weibull random variable is derived by making use of the inverse Mellin transform technique and expressed in terms of generalized hypergeometric functions. This provides computable
representations of the moment generating functions of several of the distributions that were identified as particular cases. Other statistical functions such as the cumulative distribution function of a gamma-Weibull random variable, its moments, hazard rate and associated entropy are also given in closed form. The proposed extension is utilized to model two data sets. The gamma--Weibull distribution provides a better fit than the two-parameter Weibull
model or its shifted counterpart, as measured by the Anderson-Darling and Cramer-von Mises statistics.
Al-Saqabi et al. (2003) defined a univariate gamma-type function involving the confluent hypergeometirc function of two variables (Erdélyi, 1953) and discussed some associated statistical functions. We define a bivariate generalized gamma-type function using the confluent hypergeometric
function of two variables and discuss some of its statistical functions, including the moment generating function, in terms of the G-function. This provides computable representations of the moment generating functions of
several of the distributions that were identified as particular cases. Many other distributions such as the Rayleigh, half-normal and Maxwell distributions can also be obtained as special cases of the bivariate gamma-type density function.
The cumulative distribution function is also provided in closed form.

Drinking water supply is an essential public function but is at the same time exposed to risks. Since a totally risk-free society is not attainable, risks need to be managed efficiently to achieve an acceptable level of risk. A reliable... more

Drinking water supply is an essential public function but is at the same time exposed to risks. Since a totally risk-free society is not attainable, risks need to be managed efficiently to achieve an acceptable level of risk. A reliable supply of safe drinking water is vital and the World Health Organization emphasises an integrated risk management approach, including the entire drinking water system from source to tap. An integrated approach is important as there are interactions between different parts of a system. Efficient risk management requires appropriate risk analyses to characterise risk and support decision-making. Risk analysis based on an integrated approach facilitates well-informed decision-making and efficient use of resources for risk reduction. However, guidance on methods for integrated risk analysis of drinking water systems is limited. To support risk management of drinking water systems, a method for integrated and probabilistic risk analysis has been developed...

Während meines Studiums der Wirtschaftsinformatik an der Hochschule Harz hatte ich in den Jahren 2002 bis 2005 das große Glück, als Tutor für verschiedene Statistik-Vorlesungen von Dr. Walter Strube tätig werden zu dürfen. Zu Beginn... more

Während meines Studiums der Wirtschaftsinformatik an der Hochschule Harz hatte ich in den Jahren 2002 bis 2005 das große Glück, als Tutor für verschiedene Statistik-Vorlesungen von Dr. Walter Strube tätig werden zu dürfen. Zu Beginn meiner Tutorentätigkeit konnte ich eine über die Jahre von Tutor zu Tutor weiterentwickelte Aufgabensammlung in Form einer ,,Lose-Blatt-Sammlung" von meiner direkten Vorgängerin, Frau Weinert, übernehmen. Um den Studierenden die Arbeit mit den Übungsaufgaben zu erleichtern, habe ich damals für sämtliche Aufgaben Musterlösungen und Erläuterungen verfasst und den Teilnehmern meiner Tutorien in Form von Handouts zur Verfügung gestellt. In den vergangenen sieben Jahren bin ich immer wieder von Studierenden nach dieser Sammlung von Aufgaben mit Musterlösungen gefragt worden, so dass ich mich dazu entschlossen habe, sie noch einmal zu überarbeiten, mit einigen weiteren Erläuterungen zu versehen und über den GRIN-Verlag sowie verschiedene Webseiten als kostenfreien Download zur Verfügung zu stellen. Ich hoffe, dass sie so vielleicht auch für den einen oder anderen Studierenden außerhalb unserer Hochschule von Nutzen sein kann.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or... more

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

This paper identifies the characteristics of three-parameter Burr Type XII distribution and discusses its utility in survivorship applications. It addresses the problem of estimating the three-parameter Burr XII distribution and its... more

This paper identifies the characteristics of three-parameter Burr Type XII distribution and discusses its utility in survivorship applications. It addresses the problem of estimating the three-parameter Burr XII distribution and its doubly truncated version. The results are applied on a real dataset by fitting the distribution to the survival time of breast cancer patients in the Gaza Strip. These data are known to have a heavy tailed distribution since patients in this area received different protocols of treatments in different levels of hospitals locally and abroad. The findings indicated that the estimates of the parameters of the truncated distribution are more efficient than those obtained from the original distribution since the distribution is heavy tailed and involves many highly extreme observations.

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem.... more

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ and β were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian D...

В рамках математического учения о гармонии и развернутом междисциплинарном аспекте излагается типология последовательностей Фибоначчи, основанная на синтезе математических и математико-лингвистических представлений, включающем теорию... more

В рамках математического учения о гармонии и развернутом междисциплинарном аспекте излагается типология последовательностей Фибоначчи, основанная на синтезе математических и математико-лингвистических представлений, включающем теорию рекурсии, алгебраических уравнений, непрерывных дробей, пропорций и средних. Широко используется визуализация результатов типологизации в виде орнаментальных фигур: крестов, клотоид, ветвящихся структур. Описывается широкий спектр приложений результатов типологизации в гуманитарных и естественных науках. Книга снабжена разнообразными примерами из области литературного творчества, теории ценозов, спорта, электротехники, теории поиска, физики, астрономии, экономики и архитектурного пропорционирования. Для экономистов, социологов, инженеров, филологов и других специалистов, интересующихся вопросами математической гармонии объектов произвольной природы.

Expression of the error rate for the four populations test.

A probabilistic (or statistical) experiment has the following characteristics: (a) the set of all possible outcomes of the experiment can be described; (b) the outcome of the experiment cannot be predicted with certainty prior to the... more

A probabilistic (or statistical) experiment has the following characteristics: (a) the set of all possible outcomes of the experiment can be described; (b) the outcome of the experiment cannot be predicted with certainty prior to the performance of the experiment.

The license plates system in Saudi Arabia costs millions (SAR), if not billions (SAR), but the beneciary covers most of the cost, if not all of it. In all cases, the system lacks to robustness and represents an example of impulsive... more

The license plates system in Saudi Arabia costs millions (SAR), if not billions (SAR), but the beneciary covers most of the cost, if not all of it. In all cases, the system lacks to robustness and represents an example of impulsive creation.

Some analysts believe that Bernoulli’s utility function is “reference-independent” and hence it is not able to generate a loss aversion index. This paper concludes otherwise. It posits that the geometry of Bernoulli’s original utility... more

Some analysts believe that Bernoulli’s utility function is “reference-independent” and hence it
is not able to generate a loss aversion index. This paper concludes otherwise. It posits that
the geometry of Bernoulli’s original utility function specification supports reference dependence
and a loss aversion index. It provides a solution to the open problem of closed form global
utility loss aversion index formula. Theory and evidence show that the formula follows a stable
law, and it supports a Fisher z-transform test for loss aversion. Higher order approximation of
Bernoulli’s specification of preferences predicts that a risk averse but temperate agent would
prefer a high kurtosis gamble to certainty equivalent if the payoff is sufficiently high. In contrast,
prospect theory predicts that no agent should prefer that gamble in gain domain. In a nutshell,
Bernoulli’s utility function is alive and well. It subsumes prospect theory’s skewed S-shape value
function for decision making under risk and uncertainty.

A new four-parameter model called the Marshall--Olkin ex\-ponential--Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns out to be quite flexible for... more

A new four-parameter model called the Marshall--Olkin ex\-ponential--Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns out to be quite flexible for analyzing positive data. The hazard rate functions of new model can be increasing and bathtub shaped.} Our main objectives are to obtain representations of certain statistical functions, to estimate the parameters of the proposed distribution and to discuss its modality. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson--Darling and Cram'er--von Mises goodness--of--fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.

A new four-parameter model called the gamma--exponentiated exponential--Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain... more

A new four-parameter model called the gamma--exponentiated exponential--Weibull distribution is being introduced
in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical
functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the
proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson--Darling and Cram\'{e}r--von Mises goodness--of--fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and... more

In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and exponentiated inverse Raleigh distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. We investigate the shapes of the density and hazard rate function. Some statistical properties of the new distribution including moments, mean residual life, quantile and generating functions, median, skewness and kurtosis and order statistics are discussed. The estimation of the model parameters is performed by the maximum likelihood method. The importance of the new distribution is examined through real data application and the results show that the new distribution can be useful to provide better fits than other lifetime models.

Forecasting economic growth for developing countries is a problematic task, peculiarly because of particularities they face. The model identification process in this paper yielded a random walk model for the Gross Domestic Product (GDP)... more

Forecasting economic growth for developing countries is a problematic task, peculiarly because of particularities they face. The model identification process in this paper yielded a random walk model for the Gross Domestic Product (GDP) series. We applied ARIMA models to get empirical results and bring to a close that the models obtained are suitable for forecasting the economic output of Africa. The adequate models were used for each of 20 Africa's largest economies to forecast future time series values. Based on the estimation results, we concluded that from 1990 looking forward to 2030, there will be an increasing GDP growth where the average speed of the economy of Africa will be of 5.52%, and the GDP could achieve 2185.21billionto2185.21 billion to 2185.21billionto10186.18 billion.

An obituary for the founder of 'Sociodynamics' the study of social change by using mathematical models.

Increasing the parameter of a distribution helps to capture the skewness and peakedness characteristic in the data sets. This allows a more realistic modeling of data arising from different real life situations. In this paper, we modified... more

Increasing the parameter of a distribution helps to capture the skewness and peakedness characteristic in the data sets. This allows a more realistic modeling of data arising from different real life situations. In this paper, we modified Laplace distribution using the exponentiation method. The study proved that the modified Laplace distribution (MLD) is a probability density function. Some of the basic statistical properties of the modified Laplace distribution are obtained. We applied the proposed modified Laplace distribution on two life datasets and simulated data. Parameters of the distributions were estimated using method of maximum likelihood estimation. The study compared the modified Laplace distribution with Laplace distribution and Generalized error distribution using Schwartz Criteria (SC) measure of fitness. The results obtained revealed that the modified Laplace distribution has a better fit than the Laplace and Generalized error distributions and can be used for more realistic modeling of data arising from different real life situations. The simulation results obtained shows that as the sample size increases, the Biasedness and Root Mean Square Error (RMSE) of the proposed modified Laplace distribution reduces.

"An important step in building a wind farm is to choose the most suitable turbine. The selection of the turbine involves a careful analysis of costs and technical parameters, among which stands out the capacity factor, whose calculation... more

"An important step in building a wind farm is to choose the most suitable turbine. The selection of
the turbine involves a careful analysis of costs and technical parameters, among which stands out
the capacity factor, whose calculation is performed with a statistical analysis of anemometric
records. Based on wind speed records collected in São Martinho da Serra - RS, this paper
describes an approach traditionally used in that capacity factor is the criterion of identifying the
most appropriate turbine."

We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing , bathtub and unimodal shapes. The new distribution generalizes... more

We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing , bathtub and unimodal shapes. The new distribution generalizes at least eleven lifetime models extant in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and order statistics are derived. The parameters of the new distribution are estimated by the maximum likelihood method. We illustrate empirically the superiority of the new model over other distributions by means of a real life data set.

A new generalized extended inverse Gaussian density function involving a confluent hypergeometric function is defined. Closed form representations of a generalized extended inverse Gaussian density function and the corresponding moment... more

A new generalized extended inverse Gaussian density function involving a confluent hypergeometric function is defined. Closed form representations of a generalized extended inverse Gaussian density function and the corresponding moment generating function are provided in terms of Meijer’s G-function. Some other statistical functions which are associated with the proposed distribution are also derived. Many distributions can be obtained as limiting cases of the proposed density function. This density is utilized to model an actual data set. The new distribution provides a better fit than related distributions as measured by the Anderson-Darling and Cramér-von Mises statistics. The proposed distribution could, for instance, find applications in the physical and biological
sciences and in particular be helpful to researchers working in special functions as well as reliability analysis, survival models and diffraction theory.

Goodness of fit test is a test that has attracted researchers’ interest over the decades. This study is on goodness of fit test for normal distribution only. The Kolmogorov-Smirnov (K-St) and Pearson’s Chi-square (χ² test) goodness of fit... more

Goodness of fit test is a test that has attracted researchers’ interest over the decades. This study is
on goodness of fit test for normal distribution only. The Kolmogorov-Smirnov (K-St) and Pearson’s
Chi-square (χ² test) goodness of fit test were used to determine the normality of a given data. The
result revealed that the data is normal under the two tests and that the Kolmogorov-Smirnov (K-S
test) were preferred to Pearson’s Chi-square (χ² test). The Kolmogorov-Smirnov (K-S) test of
goodness of fit is the most suitable in terms of the p-value.

In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural... more

In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural properties of the new distribution are derived including moments, moment generating function, quantile function, reliability, hazard rate function and mean residual life. Expressions for the R´enyi, q-entropies and density function of order statistics are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. Two real data sets are presented to illustrate the advantage of the new distribution. In fact, the new model provides a better fit to this data than some of the most important distributions.