Samuel Enogwe - Academia.edu (original) (raw)

Papers by Samuel Enogwe

Mathematical theory and modeling, 2021

This paper investigates a batch arrival queueing system in which customers arrives at the system ... more This paper investigates a batch arrival queueing system in which customers arrives at the system in a Poisson stream following a compound Poisson process and the system has a single server providing three types of general heterogeneous services. At the beginning of each service, a customer is allowed to choose any one of the three services and as soon as a service of any type gets completed, the server may take a vacation or may continue staying in the system. The vacation time is assumed to follow a general (arbitrary) distribution and the server vacation is based on Bernoulli schedule under a single vacation policy. During the server vacation period, impatient customers are assumed to balk. This paper described the model as a bivariate Markov chain and employed the supplementary variable technique to find closed-form solutions of the steady state probability generating function of number of customers, the steady state probabilities of various states of the system, the average queue size, the average system size, and the average waiting time in the queue as well as the average waiting time in the system. Further, some interesting special cases of the model are also derived.

In this study, a new distribution known as the Exponentiated Rama distribution has been proposed.... more In this study, a new distribution known as the Exponentiated Rama distribution has been proposed. The aim was to generalize the one parameter Rama distribution using the exponentiation technique. Some properties of proposed distribution are derived. The maximum likelihood method was used for the estimation of model parameters. The proposed distribution was subjected to real life application using a set of lifetime data and compared to Rama distribution, Exponentiated Akash distribution and Exponentiated Exponential distribution and it was found to provide the best fit than other competing distributions. Keywords: Rama distribution, Exponentiated distributions, Order statistics, Moment

Journal of Applied Mathematics and Physics

American Journal of Mathematics and Statistics, 2020

This study discusses the application of replacement model in the hotel industry. The ultimate obj... more This study discusses the application of replacement model in the hotel industry. The ultimate objective is to determine the replacement age for LED bulbs in hotel rooms. The method adopted considered cost of replacement of LED bulbs as random variables and utilized goodness-of-fit test to determine the probability distribution of replacement costs. The result showed that the LED bulbs burn for about 7.53 hours and about 78 bulbs failed per hour, resulting to an average individual replacement cost of about ₦41,600.52 per period of replacement or ₦12.47 per hour. In addition, it was observed that individual replacement of LED bulbs is required from period 1 (i.e., between 4381 and 8760 hours) through period 6 (i.e., between 26281 and 30660 hours), and after period 6 (i.e., between 26281 and 30660 hours), the group replacement is implemented with a replacement cost of about ₦54,450.00. Consequently, the study recommended the use of individual replacement policy for the hotel under inve...

European Journal of Mass Spectrometry, 2020

This paper introduces an inverse power Akash distribution as a generalization of the Akash distri... more This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-ta...

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) ... more In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

This article examines the effects of reneging, server breakdown and server vacation on the variou... more This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability ge...

European Journal of Mass Spectrometry, 2020

This paper introduces an inverse power Akash distribution as a generalization of the Akash distri... more This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-ta...

Open Journal of Statistics

International Journal of Advances in Scientific Research and Engineering

This paper presents a comprehensive review of existing techniques of k-means clustering algorithm... more This paper presents a comprehensive review of existing techniques of k-means clustering algorithms made at various times. The kmeans algorithm is aimed at partitioning objects or points to be analyzed into well-separated clusters. There are different algorithms for k-means clustering of objects such as traditional k-means algorithm, standard k-means algorithm, basic k-means algorithm, and the conventional k-means algorithm, this is perhaps the most widely used version of the k-means algorithms. These algorithms use the Euclidean distance as their metric and minimum distance rule approach by assigning each data point (objects) to its closest centroids.

Open Journal of Optimization

American Journal of Operations Research

Asian Journal of Probability and Statistics

In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted... more In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted Rama distribution. This new distribution is capable of modeling real life data with upside down bathtub shape and heavy tails. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions.

American Journal of Operations Research

American Journal of Operations Research

Mathematical theory and modeling, 2021

This paper investigates a batch arrival queueing system in which customers arrives at the system ... more This paper investigates a batch arrival queueing system in which customers arrives at the system in a Poisson stream following a compound Poisson process and the system has a single server providing three types of general heterogeneous services. At the beginning of each service, a customer is allowed to choose any one of the three services and as soon as a service of any type gets completed, the server may take a vacation or may continue staying in the system. The vacation time is assumed to follow a general (arbitrary) distribution and the server vacation is based on Bernoulli schedule under a single vacation policy. During the server vacation period, impatient customers are assumed to balk. This paper described the model as a bivariate Markov chain and employed the supplementary variable technique to find closed-form solutions of the steady state probability generating function of number of customers, the steady state probabilities of various states of the system, the average queue size, the average system size, and the average waiting time in the queue as well as the average waiting time in the system. Further, some interesting special cases of the model are also derived.

In this study, a new distribution known as the Exponentiated Rama distribution has been proposed.... more In this study, a new distribution known as the Exponentiated Rama distribution has been proposed. The aim was to generalize the one parameter Rama distribution using the exponentiation technique. Some properties of proposed distribution are derived. The maximum likelihood method was used for the estimation of model parameters. The proposed distribution was subjected to real life application using a set of lifetime data and compared to Rama distribution, Exponentiated Akash distribution and Exponentiated Exponential distribution and it was found to provide the best fit than other competing distributions. Keywords: Rama distribution, Exponentiated distributions, Order statistics, Moment

Journal of Applied Mathematics and Physics

American Journal of Mathematics and Statistics, 2020

This study discusses the application of replacement model in the hotel industry. The ultimate obj... more This study discusses the application of replacement model in the hotel industry. The ultimate objective is to determine the replacement age for LED bulbs in hotel rooms. The method adopted considered cost of replacement of LED bulbs as random variables and utilized goodness-of-fit test to determine the probability distribution of replacement costs. The result showed that the LED bulbs burn for about 7.53 hours and about 78 bulbs failed per hour, resulting to an average individual replacement cost of about ₦41,600.52 per period of replacement or ₦12.47 per hour. In addition, it was observed that individual replacement of LED bulbs is required from period 1 (i.e., between 4381 and 8760 hours) through period 6 (i.e., between 26281 and 30660 hours), and after period 6 (i.e., between 26281 and 30660 hours), the group replacement is implemented with a replacement cost of about ₦54,450.00. Consequently, the study recommended the use of individual replacement policy for the hotel under inve...

European Journal of Mass Spectrometry, 2020

This paper introduces an inverse power Akash distribution as a generalization of the Akash distri... more This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-ta...

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) ... more In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

This article examines the effects of reneging, server breakdown and server vacation on the variou... more This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability ge...

European Journal of Mass Spectrometry, 2020

This paper introduces an inverse power Akash distribution as a generalization of the Akash distri... more This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-ta...

Open Journal of Statistics

International Journal of Advances in Scientific Research and Engineering

This paper presents a comprehensive review of existing techniques of k-means clustering algorithm... more This paper presents a comprehensive review of existing techniques of k-means clustering algorithms made at various times. The kmeans algorithm is aimed at partitioning objects or points to be analyzed into well-separated clusters. There are different algorithms for k-means clustering of objects such as traditional k-means algorithm, standard k-means algorithm, basic k-means algorithm, and the conventional k-means algorithm, this is perhaps the most widely used version of the k-means algorithms. These algorithms use the Euclidean distance as their metric and minimum distance rule approach by assigning each data point (objects) to its closest centroids.

Open Journal of Optimization

American Journal of Operations Research

Asian Journal of Probability and Statistics

In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted... more In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted Rama distribution. This new distribution is capable of modeling real life data with upside down bathtub shape and heavy tails. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions.

American Journal of Operations Research

American Journal of Operations Research