Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

In this article, four bivariate exponential (BVE) distributions with subject to right censoring samples are presented. Bayesian estimates of the parameters of BVE are obtained through Linex and quadratic loss functions. Gamma prior distribution has been suggested to reforming the posterior function. The estimations and standard errors of parameters have also been obtained through simulation method. Markov chain Monte Carlo (MCMC) method is employed for the case of Block-Buse bivariate distribution because there was no closed form for estimator criteria. Simulation studies have been conducted to show that the computation parts can be implemented easily and comparing the estimated values due to two methods and with the true values as well.     

A Class of Distributions with Linear Hazard Quantile Function

In this article, we introduce and study a class of distributions that has linear hazard quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class to a real data set.     

Characterizations of the General Multivariate Weibull Distributions

For studying and modeling the time to failure of a system or component, many reliability practitioners used the hazard rate and its monotone behaviors. However, nowadays, there are two problems. First, the modern components have high reliability and, second, their distributions are usually have non monotone hazard rate, such as, the truncated normal, Burr XII, and inverse Gaussian distributions. So, modeling these data based on the hazard rate models seems to be too stringent. Zimmer et al. (1998 Zimmer , W. J. , Wang , Y. , Pathak , P. K. ( 1998 ). Log-odds rate and monotone log-odds rate distributions . J. Qual. Technol. 30 ( 4 ): 376 – 385 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Wang et al. (2003 Wang , Y. , Hossain , A. M. , Zimmer , W. J. ( 2003 ). Monotone log-odds rate distributions in reliability analysis . Commun. Statist. Theor. Meth. 32 ( 11 ): 2227 – 2244 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 2008 Wang , Y. , Hossain , A. M. , Zimmer , W. J. ( 2008 ). Useful properties of the three-parameter Burr XII distribution. In: Ahsanullah M., Applied Statistics Research Progress. pp. 11–20 . [Google Scholar]) introduced and studied a new time to failure model in continuous distributions based on log-odds rate (LOR) which is comparable to the model based on the hazard rate.

There are many components and devices in industry, that have discrete distributions with non monotone hazard rate, so, in this article, we introduce the discrete log-odds rate which is different from its analog in continuous case. Also, an alternative discrete reversed hazard rate which we called it the second reversed rate of failure in discrete times is also defined here. It is shown that the failure time distributions can be characterized by the discrete LOR. Moreover, we show that the discrete logistic and log logistics distributions have property of a constant discrete LOR with respect to t and ln t, respectively. Furthermore, properties of some distributions with monotone discrete LOR, such as the discrete Burr XII, discrete Weibull, and discrete truncated normal are obtained.     

An extension of the exponential distribution

A generalization of the exponential distribution is presented. The generalization always has its mode at zero and yet allows for increasing, decreasing and constant hazard rates. It can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. A comprehensive account of the mathematical properties of the generalization is presented. A real data example is discussed to illustrate its applicability.     

Some properties of hazard rate functions of systems with two components

In this paper we compare the hazard rate functions of two parallel systems, each of which consists of two independent components with exponential distribution functions. The paper gives various conditions under which there exists a hazard rate ordering between the two parallel systems. It is also shown that some of these conditions are both sufficient and necessary. In particular, it is proven that if the vector consisting of the two hazard rates of the two exponential components in one parallel system weakly supmajorizes the counterpart of the other parallel system, then the first parallel system is greater than the second parallel system in the hazard rate ordering. This paper further compares the hazard rate functions of two parallel systems when both systems have components following a certain bivariate exponential distribution.     

A new generalization of the Weibull-geometric distribution with bathtub failure rate

In this paper, the researchers attempt to introduce a new generalization of the Weibull-geometric distribution. The failure rate function of the new model is found to be increasing, decreasing, upside-down bathtub, and bathtub-shaped. The researchers obtained the new model by compounding Weibull distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains some previously known lifetime distributions as well as a new one. Some basic distributional properties and moments of the new model are discussed. Estimation of the parameters is illustrated and the model with two known real data sets is examined.     

Minimum Risk Estimation of Scalar Means under Convex Combination of Loss Functions

We derive the minimum risk estimates of the scalar means for Normal, Exponential, and Gamma distributions, under the convex combination of SEL and LINEX loss functions. The functional forms of the proposed estimates for the three examples are general in nature, and for the boundary conditions provide us with the corresponding estimates under SEL and LINEX loss, respectively. We authenticate our proposed models using different iterative as well as meta-heuristic techniques, and through extensive simulation as well as application of live data sets, validate the efficacy of our proposed results.     

A new four-parameter discrete distribution with bathtub and unimodal failure rate

In this paper, a discrete counterpart of the general class of continuous beta-G distributions is introduced. A discrete analog of the beta generalized exponential distribution of Barreto-Souza et al. [2], as an important special case of the proposed class, is studied. This new distribution contains some previously known discrete distributions as well as two new models. The hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Some distributional and moment properties of the new distribution as well as its order statistics are discussed. Estimation of the parameters is illustrated using the maximum likelihood method and, finally, the model with a real data set is examined.     

A new discrete distrlbution,with applications to survival,dispersal and dispersion

We describe a new discrete probability distribution with several useful properties for the analysis and modelling of survival processes and dispersion. First, the model can be used to describe survival processes with monotonically decreasing, constant, or increasing hazard functions, simply by tuning one parameter. Also, the model can describe counts that are overdispersed (contagious) or underdispersed, since the variance can exceed, equal, or be less than the mean. All of these properties are demonstrated both theoretically and with ecological examples, using ad-hoc parameter estimation techniques. Finally, the equations are tractable compared with, say, the negative binomial, and easily incorporated into larger models.