Finite Range Distributions Research Articles

On some characterization results of -norm dynamic survival entropies

The information based on entropy of uncertainty associated with the residual life of a random variable is implemented in various fields, e.g., information theory, statistical physics, reliability theory, statistics, demography and economics, etc. In this paper, we propose two new -norm dynamic survival entropy (RNDSE) and -norm weighted dynamic survival entropy (RNWDSE) based on the survival function and some results on stochastic ordering are studied in detail. Further, we have investigated the bounds on RNDSE and RNWDSE in terms of failure rate function. In addition, some relationships between RNDSE, RNWDSE and failure function have also been well established. Finally, in order to illustrate the applications of RNDSE and RNWDSE, some useful distributions like exponential, Rayleigh, Weibull, Pareto, finite range distributions and one new distribution called T-exponential have been characterized.

Inference Based on Type-II Hybrid Censored Data from a Pareto Distribution

The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular failures to be observed by the end of the experiment. Maximum likelihood and Bayes estimation methods are used with their approximate confidence intervals. Proposed estimation methods are compared numerically based on simulation studies. A numerical example is also used to illustrate the theoretical outcomes.

Quantile-Based Generalized Entropy of Order (α, β) for Order Statistics

In the present paper, we propose a quantile version of generalized entropy measure for order statistics for residual and past lifetimes and study their properties. Lower and upper bound of the proposed measures are derived. It is shown that the quantile-based generalized information between i-th order statistics and parent random variable is distribution free. The uniform, exponential, generalized Pareto and finite range distributions, which are commonly used in the reliability modeling have been characterized in terms of the proposed entropy measure with extreme order statistics.

Characterization of Lifetime Distribution Based on Generalized Interval Entropy

In this paper, we introduce the concept of generalized interval entropy measure of order alpha and type beta for the doubly truncated random variable. A characterization problem for the generalized interval entropy measure has been studied. The exponential, the pareto and finite range distributions have been characterized in terms of the proposed entropy measure and generalized failure rate function. A lower bound to generalized interval entropy has also been derived. Finally some stochastic comparison based on generalized interval entropy are presented.

Some Results on Dynamic Generalized Survival Entropy

Recently, Zografos and Nadarajah (2005) proposed two measures of uncertainty based on the survival function, called the survival exponential entropy and the generalized survival exponential entropy. In this article, we explore properties of the generalized survival entropy and the dynamic version of it. We study conditions under which the generalized survival entropy of first order statistic can uniquely determines the parent distribution. The exponential, Pareto, and finite range distributions, which are commonly used in reliability, have been characterized using this generalized measure. Another measure of entropy is also introduced in analogy with cumulative entropy which has been proposed by Di Crescenzo and Longobardi (2009) and some properties of it are given.

On study of dynamic survival and cumulative past entropies

Recently, a new class of measure of uncertainty, called “dynamic survival entropy”, has been defined and studied in the literature. Based on this entropy, DSE(α) ordering, IDSE(α), and DDSE(α) classes of life distributions are defined and some results are studied. In this paper, our main aim is to prove some more results of the ordering and the aging classes of life distributions mentioned above. Some important distributions such as exponential, Pareto, Pareto II, and finite range distributions are also characterized. Here we have defined cumulative past entropy and proved some interesting results.

Some characterization results on generalized cumulative residual entropy measure

The cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon entropy, refer to Rao et al. (2004). In this paper we study a generalized cumulative residual information measure based on Verma’s entropy function and a dynamic version of it. The exponential, Pareto and finite range distributions, which are commonly used in reliability modeling, have been characterized using this generalized measure.

A Generalization of the Lack of Memory Property and Related Characterization Results

The lack of memory property uniquely determines the exponential distribution and plays a vital role in the classification of life distributions. Some stochastic versions of the same are also available in the literature. The present article introduces a generalized lack of memory property and characterizes from it the exponential distribution, the Lomax distribution, and a finite range distribution. The corresponding stochastic version has also been presented. Attempts have also been made to extend this generalized lack of memory property in the bivariate set-up and determine bivariate distributions from the same.

Bivariate Characterized Model Based on Mean Residual Life Properties

This paper uses the concept of characterized model for bivariate extensions of univariate life distributions based on mean residual life properties. Different bivariate distributions can be generated from different choices of marginal distributions. The retention of univariate IMRL, DMRL, NBUE, NWUE, HNBUE and HNWUE class properties in the bivariate setup has been ensured along with results of importance for reliability analysis. A characterization of the exponential, Lomax and finite range distributions has been obtained in this process.

Bayesian analysis of reliability and hazard rate function of a mixture model

The present article deals with the Bayesian analysis for a modified (general) Mukherji-Islam model [A finite range distribution of failure times, Naval Research Logistics Quarterly, 1983, 30, 487–491] on the basis of failure time data x 1, x 2, …, x r for a prefixed number of failures. Under the use of different prior densities for the parameter and the squared error loss function (SELF), the Bayesian estimates of hazard rate and the reliability functions are obtained, considering uniform, Gamma and inverted gamma densities as prior failure densities.

Bivariate Extension of Lomax and Finite Range Distributions through Characterization Approach

In the univariate setup the Lomax distribution is being widely used for stochastic modelling of decreasing failure rate life components. It also serves as a useful model in the study of labour turnover, queueing theory, and biological analysis. A bivariate extension of the Lomax distribution given in Lindley and Singpurwalla (1986) fails to cover the case of independence. Our present attempt is to obtain the unique determination of a bivariate Lomax distribution through characterization results. In this process we also obtain bivariate extensions of the exponential and a finite range distributions. The bivariate Lomax distribution thus obtained is a member of the Arnold (1990) flexible family of Pareto distributions and the bivariate exponential distribution derived here is identical with that of Gumbel (1960). Various properties of the proposed extensions are presented.

Characterizations by properties of residual life distributions

In this paper we use certain properties of bivariate residual life distributions to characterize the bivariate exponential, Pareto and finite range distributions.

Characterizations of Bivariate Lomax and Finite Range Distributions

In this note we characterize the bivariate Lomax and bivariate finite range distributions using the forms of their marginal and conditional distributions of the same component and also by the forms of certain conditional distributions.

Selection of probability distribution for life testing data

A procedure for choosing between models from two families of distributions for failure data is given. This method is based on F-statistics and can be used for a non-censored set of life testing observations. Monte Carlo samples from exponential , Wei bull , Pareto and finite range distributions are used. The performance of the proposed procedure is compared to the selection procedure S, derived by Quesenberry and Kent (1982)and to the MLR test considered by Bain and Engelhardt (l980).

Some Characterizations of the Exponential and Related Life Distributions

Characterizations of the exponential, the Pearsonian Type XI and a finite range distributions have been obtained in terms of different constant coefficients of variation of residual life. These results have also been stated in terms of conditional expectations of suitably chosen functions of order statistics. A few earlier results have been generalised. Some related results in IMRL and DMRL. classes of distributions have been presented . Also characterizations involving the product of failure rate and mean residual life are aiven.

A note on “A finite range distribution of failure times”

A finite-range life distribution is proposed and studied by Mukherjee & Islam [6]. Due to an unfortunate oversight, some errors have occurred in discussing aging properties of this distribution. We rectify the mistakes and bring to light some other interesting properties of this distribution.

The Chebyshev center: A multidimensional estimate of location

In this paper the center of the smallest k-dimensional sphere enclosing a data set, hereinafter called the Chebyshev center, is introduced as a multidimensional measure of location. The distribution of this estimator, which is a multidimensional generalization of the univariate midrange, is derived in the general case and its properties investigated for a host of distributions. The Chebyshev center is shown to be a maximum likelihood estimator for the center of a uniform distribution over a k-sphere and both unbiased and consistent for the multivariate spherical normal distribution and any spherical finite range distribution.

Singularities of the generator-coordinate amplitude for scattering

It is shown that the high-frequency catastrophe which plagues generator-coordinate calculations is a finite-range distribution. This finite range allows standard numerical procedures matching an internal solution with an asymptotic external wave.