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The class of transmuted distributions has received a lot of attention in the recent statistical literature. In this paper, we propose a rich family of bivariate distribution whose condition...

Quantile-based reliability analysis has received much attention recently. We propose new quantile-based tests for exponentiality against decreasing mean residual quantile function (DMRQ) and new better than used in expectation (NBUE) classes of alternatives. The exact null distribution of the test statistic is derived when the alternative class is DMRQ. The asymptotic properties of both the test statistics are studied. The performance of the proposed tests with other existing tests in the literature is evaluated through simulation study. Finally, we illustrate our test procedure using real data sets.

The notion of cascading failures is a common phenomenon we observe around us. Here the initial failure alters the structure function of the system, which leads to subsequent failures within a short period of time referred to as threshold time. [17] introduced the concept of cascading failures within the framework of reliability theory. Swift [24] extended the Freund bivariate exponential distribution to model cascading failures. The Freund bivariate exponential distribution [10] allows to model a parallel redundant system with two components. In this system the lifetimes of the two components behave as if they are independent, until one of the components fail, after which the remaining component suffers an increased/decreased stress. In this paper we further study the model of Swift [24]. Various properties of the model are investigated and statistical inference procedures are developed using L-moments and method of moments. A practical application of this model is illustrated using data from www....

SYNOPTIC ABSTRACTSeveral authors have considered the analysis of load-sharing parallel systems. The main characteoristics of such a two-component system is that after the failure of one component, the surviving component has to shoulder extra load, and hence, it is more likely to fail earlier than would be expected under the original model. In other cases, the failure of one component may release extra resources to the other component, thus delaying the system failure. Freund introduced a bivariate extension of the exponential distribution, which is applicable to two-component load-sharing systems. It is based on the assumption that the lifetime distributions of the components are exponential random variables before and after the change. In this article, we introduce a new class of bivariate distribution using the proportional hazard model. It is observed that the bivariate model proposed by Freund is a particular case of our model. We study different properties of the proposed model. Different statistica...

L-moments are expectations of linear combinations of order statistics, their use in reliability analysis has been established. In the present paper we study L-moments in relation to income inequality measures. Models characterized by functional relationships between L-moments and income inequality measures are studied. Finally, we define the ordering based on L-moments and study its implications on other existing orderings.

The present paper aims at studying the mean past lifetime of a discrete random variable. The notion of discrete mean past lifetime is studied in relation to the concepts of reversed hazard rate, reversed lack of memory property, and cumulative past entropy. New classes of distributions characterized by particular forms of discrete mean past life are also investigated. Implications of an increasing mean past lifetime on other reliability notions are studied and finally some bivariate generalizations are discussed.

It is reasonable to presume that in many realistic situations uncertainty is not necessarily related to the future but can also refer to the past. A measure of uncertainty in this context is the cumulative entropy defined for a non-negative random variable. In this paper we extend this definition to the case of a distributions with support in $$\mathbb {R}$$ . Conditions for the existence of this measure and its properties are also considered. Apart from this, certain characterization results based on past entropy measures are also discussed.

Abtsrcat In the univariate case Lorenz order and related summary measures of inequality such as the Gini Index seem to be quite generally accepted as appropriate indicators of inequality. Several extensions of the Lorenz order and Gini index to the multivariate setup has been proposed by various authors. The choice of an apt measure depends on the dependence enjoyed by the original bivariate distribution. When the distribution has a load sharing dependence it is more adequate to study the univariate conditional distributions than the joint distributions. In this paper we study the inequality measures specifically, Lorenz function and Gini index of these distributions and characterize the original bivariate distribution using these measures.

A binary operator ∗ over real numbers is said to be associative if ( x ∗ y ) ∗ z = x ∗ ( y ∗ z ) and is said to be reducible if x ∗ y = x ∗ z if and only if y = z and if y ∗ w = z ∗ w if and only if y = z . The operation is said to have an identity element e if x ∗ e = x . In this paper a characterization of a subclass of the reversed generalized Pareto distribution [Castillo, E. Hadi, A.S., 1995. Modelling life time data with applications to fatigue models. Journal of American Statistical Association. 90 (431), 1041–1054] is generalized using this operator. The idea is extended to the bivariate case too and it is shown that it characterizes a class of bivariate distributions containing the characterized extension (CE) model of Roy [Roy, D. 2002a. A characterization of model approach for generating bivariate life distributions using reversed hazard rates. Journal of Japan Statistical Society 32 (2), 239–245].

Block et.al (1998) studied the properties of the reversed hazard rate (rhr) and characterized a class of distributions having constant rhr in its interval of support. In this paper we study another equivalent characterization of this class along with its bivariate extensions.

The concept of the univariate mean residual life (mrl) function is generalized to the bivariate case in the discrete set up and its properties are studied. This bivariate mrl is utilized to characterize bivariate distributions by its functional form .

In this article, we investigate models that exhibit constant total failure rate (Sun, K., Basu, A. P. (1995). A characterization of a bivariate geometric distribution. Statistics and Probability Letters 23:307–311) and study the property in relation to the bivariate lack of memory property (BLMP).

In this paper two characterizations in terms of the properties of the residuai life distribution of a bivariate seometric model is established.

In this paper an expository analysis of three definitions of bivariate failure rates in the discrete time domain is attempted. Conditions under which each rate determines the distribution of failure times uniquely are investigated. Further, some characterizations of bivariate distributions based on the functional forms of these rates are established.

New classes of multivariate survival distribution functions based on monotonic behaviour of a multivariate failure rate are developed in the discrete set up. Relationship among the classes along with multivariate geometric distributions that act as boundaries of the various classes are identified.