scholarly journals Discreteweighted exponential distribution: Properties and applications

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 3043-3056 ◽  
Author(s):  
Mahdi Rasekhi ◽  
Omid Chatrabgoun ◽  
Alireza Daneshkhah
Keyword(s):  
Exponential Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Moment Generating Function ◽  
Strength Parameter ◽  
Discrete Version ◽  
Lifetime Distributions ◽  
Reliability Indices ◽  
Rate Functions ◽  
Maximum Likelihood Estimations

In this paper, we propose a new lifetime model as a discrete version of the continuous weighted exponential distribution which is called discrete weighted exponential distribution (DWED). This model is a generalization of the discrete exponential distribution which is originally introduced by Chakraborty (2015). We present various statistical indices/properties of this distribution including reliability indices, moment generating function, probability generating function, survival and hazard rate functions, index of dispersion, and stress-strength parameter. We first present a numerical method to compute the maximum likelihood estimations (MLEs) of the models parameters, and then conduct a simulation study to further analyze these estimations. The advantages of the DWED are shown in practice by applying it on two real world applications and compare it with some other well-known lifetime distributions.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals Transient Solution of 𝑀𝑋/𝑀/𝐶 Queueing Model for Homogenous Servers, with Catastrophes, Balking & Vacation

2020 ◽  
Vol 5 (4) ◽  
pp. 65-69
Author(s):  
G. Kavitha ◽  
◽  
K.Julia Rose Mary ◽  
Keyword(s):  
Exponential Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Service Rate ◽  
Queueing Model ◽  
Transient Solution

In this paper we analyze 𝑴𝑿/𝑴/𝑪 Queueing model of homogenous service rate with catastrophes, balking and vacation. Here we consider the customers, where arrival follow a poisson and the service follows an exponential distribution. Based on the above considerations, under catastrophes, balking and vacation by using probability generating function along with the Bessel properties we obtain the transient solution of the model in a simple way.

Some exact distributions in traffic noise theory

1975 ◽  
Vol 7 (03) ◽  
pp. 593-606 ◽  
Author(s):  
Allan H. Marcus
Keyword(s):  
Exponential Distribution ◽  
Generating Function ◽  
Noise Intensity ◽  
Traffic Noise ◽  
Domain Of Attraction ◽  
Moment Generating Function ◽  
Stable Law ◽  
Doubly Stochastic ◽  
Exact Distributions ◽  
The Moment

The moment-generating function of the traffic noise from a stream of vehicles with identical noise emissions cannot be readily inverted. If the emissions are not equal, this generating function can be inverted to obtain the exact form of the distribution function in some particular cases. Noise intensity has a maximally skew stable distribution with exponent 1/2 for observers on the highway, whatever the distribution of emissions. The distribution at any distance from the highway is an exponentially modified stable law with exponent 1/2 for an improper exponential distribution of emissions, and an infinite series involving this stable law and iterated error functions when emissions have an exponential distribution. A doubly stochastic process for emissions produces distributions of traffic noise intensity in the domain of attraction of skew stable laws with exponent α, 1/2 < α < 2. The inverse Gaussian (exponentially modified skew stable law with exponent 1/2) is recommended as the best choice of a two-parameter family for fitting traffic noise intensity distributions.

scholarly journals Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process

2021 ◽  
Vol 26 (4) ◽  
pp. 76
Author(s):  
Muhammed Rasheed Irshad ◽  
Christophe Chesneau ◽  
Veena D’cruz ◽  
Radhakumari Maya
Keyword(s):  
Generating Function ◽  
Simulation Study ◽  
Probability Generating Function ◽  
Autoregressive Process ◽  
Discrete Version ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
First Order ◽  
Mathematical Properties

In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets.

scholarly journals The alpha power Teissier distribution and its applications

2021 ◽  
Vol 16 (2) ◽  
pp. 2733-2747
Author(s):  
Joseph Thomas Eghwerido
Keyword(s):  
Data Analysis ◽  
Generating Function ◽  
Hazard Rate ◽  
Real Life ◽  
Probability Generating Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model

Statistical distribution that represents the true characteristics of real-life data is paramount to data analysis. Thus, this study introduces a tractable alpha power Teissier distribution (APOT). Some statistical properties of the proposed model like moments, probability generating function, moment generating function and order statistic were examined. The shape of the hazard rate and survival functions were investigated. The shapes of the hazard rate function indicated increasing, decreasing, J-shaped and bathtub shapes. The results of the data analysis indicated that the APOT model performed better when compared to some existing classical statistical distributions.

Bounded M-O Extended Exponential Distribution with Applications

2019 ◽  
Vol 34 (1) ◽  
pp. 35-51
Author(s):  
Indranil Ghosh ◽  
Sanku Dey ◽  
Devendra Kumar
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Generating Function ◽  
Hazard Rate ◽  
Real Data ◽  
Moment Generating Function ◽  
Residual Lifetime ◽  
Model Parameters ◽  
Data Sets ◽  
Conditional Moment Generating Function

Abstract In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95  asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

Some exact distributions in traffic noise theory

1975 ◽  
Vol 7 (3) ◽  
pp. 593-606 ◽  
Author(s):  
Allan H. Marcus
Keyword(s):  
Exponential Distribution ◽  
Generating Function ◽  
Noise Intensity ◽  
Traffic Noise ◽  
Domain Of Attraction ◽  
Moment Generating Function ◽  
Stable Law ◽  
Doubly Stochastic ◽  
Exact Distributions ◽  
The Moment

The moment-generating function of the traffic noise from a stream of vehicles with identical noise emissions cannot be readily inverted. If the emissions are not equal, this generating function can be inverted to obtain the exact form of the distribution function in some particular cases. Noise intensity has a maximally skew stable distribution with exponent 1/2 for observers on the highway, whatever the distribution of emissions. The distribution at any distance from the highway is an exponentially modified stable law with exponent 1/2 for an improper exponential distribution of emissions, and an infinite series involving this stable law and iterated error functions when emissions have an exponential distribution. A doubly stochastic process for emissions produces distributions of traffic noise intensity in the domain of attraction of skew stable laws with exponent α, 1/2 < α < 2. The inverse Gaussian (exponentially modified skew stable law with exponent 1/2) is recommended as the best choice of a two-parameter family for fitting traffic noise intensity distributions.

scholarly journals Multi-Objective Electrical Power System Design Optimization Using a Modified Bat Algorithm

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3956
Author(s):  
Khaled Guerraiche ◽  
Latifa Dekhici ◽  
Eric Chatelet ◽  
Abdelkader Zeblah
Keyword(s):  
Power Systems ◽  
Electrical Power ◽  
Bat Algorithm ◽  
Moment Generating Function ◽  
Electrical Power System ◽  
System Availability ◽  
Reliability Indices ◽  
Multi Objective ◽  
Investment Cost ◽  
Modified Bat Algorithm

The design of energy systems is very important in order to reduce operating costs and guarantee the reliability of a system. This paper proposes a new algorithm to solve the design problem of optimal multi-objective redundancy of series-parallel power systems. The chosen algorithm is based on the hybridization of two metaheuristics, which are the bat algorithm (BA) and the generalized evolutionary walk algorithm (GEWA), also called BAG (bat algorithm with generalized flight). The approach is combined with the Ushakov method, the universal moment generating function (UMGF), to evaluate the reliability of the multi-state series-parallel system. The multi-objective design aims to minimize the design cost, and to maximize the reliability and the performance of the electric power generation system from solar and gas generators by taking into account the reliability indices. Power subsystem devices are labeled according to their reliabilities, costs and performances. Reliability hangs on an operational system, and implies likewise satisfying customer demand, so it depends on the amassed batch curve. Two different design allocation problems, commonly found in power systems planning, are solved to show the performance of the algorithm. The first is a bi-objective formulation that corresponds to the minimization of system investment cost and maximization of system availability. In the second, the multi-objective formulation seeks to maximize system availability, minimize system investment cost, and maximize the capacity of the system.

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