scholarly journals A New Family of Bivariate Exponential Distributions with Negative Dependence Based on Counter-Monotonic Shock Method

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 548
Author(s):  
Rachid Bentoumi ◽  
Farid El Ktaibi ◽  
Mhamed Mesfioui
Keyword(s):  
Lower Bound ◽  
Method Of Moments ◽  
Bivariate Distribution ◽  
Negative Dependence ◽  
Shock Model ◽  
Exponential Distributions ◽  
Positive Dependence ◽  
New Family ◽  
Distributional Properties ◽  
Bivariate Exponential

We introduce a new family of bivariate exponential distributions based on the counter-monotonic shock model. This family of distribution is easy to simulate and includes the Fréchet lower bound, which allows to span all degrees of negative dependence. The construction and distributional properties of the proposed bivariate distribution are presented along with an estimation of the parameters involved in our model based on the method of moments. A simulation study is carried out to evaluate the performance of the suggested estimators. An extension to the general model describing both negative and positive dependence is sketched in the last section of the paper.

Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

scholarly journals An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2064
Author(s):  
Sadaf Khan ◽  
Oluwafemi Samson Balogun ◽  
Muhammad Hussain Tahir ◽  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi
Keyword(s):  
Exponential Family ◽  
Simulation Analysis ◽  
Structural Characteristics ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Risk Theory ◽  
Data Sets ◽  
Exponential Distributions ◽  
New Family ◽  
Lehmann Alternative

In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family’s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family’s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.

Reliability assessment of the standby system with dependent components by bivariate exponential distributions

2021 ◽  
pp. 1748006X2110414
Author(s):  
Afshin Yaghoubi ◽  
Peyman Gholami
Keyword(s):  
Reliability Function ◽  
Active Components ◽  
Exponential Distributions ◽  
Bivariate Exponential Distribution ◽  
Multiple Components ◽  
Proposed Model ◽  
Bivariate Exponential ◽  
Real World Applications ◽  
Model Dependency ◽  
Reduced Time

In the reliability analysis of systems, all system components are often assumed independent and failure of any component does not depend on any other component. One of the reasons for doing so is that considerations of calculation and elegance typically pull in simplicity. But in real-world applications, there are very complex systems with lots of subsystems and a choice of multiple components that may interact with each other. Therefore, components of the system can be affected by the occurrence of a failure in any of the components. The purpose of this paper is to give an explicit formula for the computation of the reliability of a system with two parallel active components and one spare component. It is assumed that parallel components are dependent and operate simultaneously. Two distributions of Freund’s bivariate exponential and Marshall–Olkin bivariate exponential are used to model dependency between components. The results show that the reliability of the system with Freund’s bivariate exponential distribution has lower reliability. The circumstances that lead to them, namely load-sharing in the case of Freund, results in lower reliability. Finally, a numerical example is solved to evaluate the proposed model and sensitivity analysis is performed on the system reliability function. The obtained results show that because the proposed model is influenced by the dependency, compared to traditional models, it has the characteristic of leading to reduced time to (first) failure for achieving specified reliability.

scholarly journals On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 953
Author(s):  
Rashad A. R. Bantan ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
Mohammed Elgarhy
Keyword(s):  
Statistical Models ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Exponential Distributions ◽  
New Family ◽  
Proposed Model ◽  
Complete Study ◽  
Probability And Statistics ◽  
Definition Of ◽  
Analyze Data

This paper develops the exponentiated Mfamily of continuous distributions, aiming to provide new statistical models for data fitting purposes. It stands out from the other families, as it depends on two baseline distributions, with the use of ratio and power transforms in the definition of the main cumulative distribution function. Thanks to the joint action of the possibly different baseline distributions, flexible statistical models can be created, motivating a complete study in this regard. Thus, we discuss the theoretical properties of the new family, with emphasis on those of potential interest to the overall probability and statistics. Then, a new three-parameter lifetime distribution is derived, with the choices of the inverse exponential and exponential distributions as baselines. After pointing out the great flexibility of the related model, we apply it to analyze an actual dataset of current interest: the daily COVID-19 cases observed in Pakistan from 21 March to 29 May 2020 (inclusive). As notable results, we demonstrate that the proposed model is the best among the 15 top ranked models in the literature, including the inverse exponential and exponential models, several modern extensions of them depending on more parameters, and the “unexponentiated” version of the proposed model as well. As future perspectives, the proposed model can be of interest to analyze data on COVID-19 cases in other countries, for possible comparison studies.

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (01) ◽  
pp. 48-61
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

Correlated reliability and an application: Propulsive landing on Mars

2019 ◽  
Vol 233 (5) ◽  
pp. 826-846
Author(s):  
Hüseyin Sarper
Keyword(s):  
System Reliability ◽  
Simulation Method ◽  
The Other ◽  
Simulation Methods ◽  
Exponential Distributions ◽  
Numerical Examples ◽  
Beneficial Effects ◽  
Bivariate Exponential ◽  
System Life ◽  
Near Future

This article discusses reliability of landers and provides a review and examples of correlated reliability. Examples are cited to show generally beneficial effects of correlation in system reliability. Then, reliabilities of two near future landing systems are studied using two analytical (Downton, and Marshall & Olkin) bivariate exponential distributions and two simulation methods that incorporate correlation in reliability calculations. Both landing systems are composed of correlated two-unit subsystems. Numerical examples show mean system life, standard deviation of the system life, mean system life confidence interval, and reliability for each lander’s propulsive descent. Both simulation method results are in between the results obtained from the two analytical methods and Downton’s method yields the most conservative reliability. This article also shows how the Downton method–based reliability value can be predicted as a function of the reliabilities obtained from the other three methods. An up-to-date literature review of all related topics is also provided.

scholarly journals Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 358 ◽  
Author(s):  
M. S. Eliwa ◽  
Ziyad Ali Alhussain ◽  
M. El-Morshedy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Discrete Analogue ◽  
Likelihood Method ◽  
New Family ◽  
Distributional Properties ◽  
Reliability Characteristics ◽  
Proposed Model ◽  
The Family ◽  
Family Of Distributions

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

Mixture of Bivariate Exponential Distributions

2010 ◽  
Vol 39 (15) ◽  
pp. 2711-2720 ◽  
Author(s):  
Norou Diawara ◽  
Mark Carpenter
Keyword(s):  
Exponential Distributions ◽  
Bivariate Exponential
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