Class Of Lifetime Distributions Research Articles

On Weighted Generalized Cumulative Residual Entropy of Order n

The present paper considers a shift-dependent measure of uncertainty and its dynamic (residual) version. Various properties have been discussed. Two classes of lifetime distributions are proposed. Further, when m independent and identically distributed observations are available, an estimator of the measure under study is presented using empirical approach. In addition, large sample properties of the estimator are studied. Finally, an application of the proposed measure to the problem related to right-tail risk measure is presented.

A New Family of Topp and Leone Geometric Distribution with Reliability Applications

In this paper, a new class of lifetime distribution, which is called Topp–Leone (J-shaped) geometric distribution, is obtained by compound of the Topp–Leone and geometric distributions. Reliability and statistical properties of the new distribution such as quantiles, moment, hazard rate, reversed hazard rate, mean residual life, mean inactivity time, entropies, moment generating function, order statistics and their stochastic orderings are obtained. Estimation of the model parameters by least squares, weighted least squares, maximum likelihood and the observed information matrix are derived. Finally, a real data set is analyzed for illustrative purposes.

A complementary generalized linear failure rate-geometric distribution

ABSTRACTIn this article, we shall attempt to introduce a new class of lifetime distributions, which enfolds several known distributions such as the generalized linear failure rate distribution and covers both positive as well as negative skewed data. This new four-parameter distribution allows for flexible hazard rate behavior. Indeed, the hazard rate function here can be increasing, decreasing, bathtub-shaped, or upside-down bathtub-shaped. We shall first study some basic distributional properties of the new model such as the cumulative distribution function, the density of the order statistics, their moments, and Rényi entropy. Estimation of the stress-strength parameter as an important reliability property is also studied. The maximum likelihood estimation procedure for complete and censored data and Bayesian method are used for estimating the parameters involved. Finally, application of the new model to three real datasets is illustrated to show the flexibility and potential of the new model compared to rival models.

A new class of lifetime distributions

In this paper, a new class of lifetime distributions which is obtained by compounding arbitrary continuous lifetime distribution and discrete phase-type distribution is introduced. In particular, the class of exponential-phase type distributions is studied with some details.

The Additive Weibull-Geometric Distribution: Theory and Applications

In this paper, we introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution. This distribution obtained by compounding the additive Weibull and geometric distributions. The new distribution has a number of well-known lifetime special sub-models such as modified Weibull geometric, Weibull geometric, exponential geometric, among several others. Some structural properties of the proposed new distribution are discussed. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

Generalized linear failure rate power series distribution

In this article, we introduce a new class of lifetime distributions. This new class includes several previously known distributions such as those of Chahkandi and Ganjali (2009), Mahmoudi and Jafari (2012), and Nadarajah et al. (2012). This new class of four-parameter distributions allows for flexible failure rate behavior. Indeed, the failure rate function here can be increasing, decreasing, bathtub-shaped or upside-down bathtub-shaped. Several distributional properties of the new class including moments, quantiles and order statistics are studied. An EM algorithm for computing the estimates of the parameters involved is proposed and some maximum entropy characterizations are discussed. Finally, to show the flexibility and potential of the new class of distributions, applications to two real data sets are provided.

New multivariate aging notions based on the corrected orthant and the standard construction

ABSTRACTRecently, some well-known univariate aging classes of lifetime distributions have been characterized by means of properties of their quantile functions and excess-wealth functions. The generalization of the univariate aging notions to the multivariate case involve, among other factors, appropriate definitions of multivariate quantiles or regression representation and related notions, which are able to correctly describe the intrinsic characteristic of the concepts of aging that should be generalized. The multivariate versions of these notions, which are characterized by using the multivariate u-quantiles and the multivariate excess-wealth function, are considered in this paper. Relationships between such multivariate aging classes are studied, and examples are provided.

A unified class of compound lifetime distributions

A flexible class of lifetime distributions is obtained by compounding the first activation and the last activation survival functions proposed by Rodrigues et al. (2011), which possess nice biological and physical interpretations. In this compound scheme, the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. We demonstrate that several models recently introduced in the literature can be derived as special cases of the proposed model.

The modified Weibull geometric distribution

A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes.

Quasi Lindley Geometric Distribution

paper, we introduce a new class of lifetime distributions which is called the Quasi Lindley Geometric (QLG) distribution. This distribution obtained by compounding the Quasi Lindley and geometric distributions. Some structural properties of the proposed new distribution are discussed, including probability density function and explicit algebraic formulas for its survival and hazard functions, moment , moment generating function and mean deviations. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution. KeywordsLindley distribution, Geometric distribution, Moments, Maximum likelihood

Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.

Reliability Analysis of $k$-out-of-$n$ Systems With Single Cold Standby Using Pearson Distributions

k-out-of-n systems with cold standby units are typically studied for unit lifetime distributions that allow analytical tractability. Often, however, these distributions differ significantly from reality. In this paper, we present an analytical approach to compute the mean failure time for k -out-of-n systems with a single cold standby unit for the wide class of lifetime distributions that can be captured by the Pearson distribution. The method requires the first four statistical moments of the unit's lifetime distribution to be given, and computes the mean failure time using the Pearson distribution as an intermediate vehicle during the numerical integration. Experimental results for various instances of the Weibull distribution show that the numerical accuracy of the approach is high, with less than 0.5 percent error across a large range of k -out-of-n systems.

An exponentiated exponential binomial distribution with application

A new continuous distribution is introduced by compounding exponentiated exponential and binomial distributions, named as exponentiated exponential binomial (EEB) distribution. This distribution has the ability to model lifetime data with increasing, decreasing and upside-down bathtub shaped failure rates. Moreover, the zero-truncated binomial distribution used in compounding is overdispersed. Some properties of the distribution are investigated. Estimation and inference procedure for the distribution parameters are discussed. An application to real data demonstrates that the EEB distribution can provide a better fit than a recent class of lifetime distributions.

Preservation properties of a homogeneous Poisson process stopped at an independent random time

To study the ageing and stochastic properties of lifetime random variables, several classes of lifetime distributions have been defined in reliability literature. In this context, an interesting problem is then to investigate the closure properties of such classes under different operators. In this paper, we study the preservation properties of classes of increasing mean inactivity time (IMIT), increasing variance inactivity time (IVIT), and some other recently introduced classes, such as NRBU, NRBUE, and NBRUrh, under a Poisson process stopped at a random time. We also analyze the preservation properties of Poisson shock models for the above-mentioned ageing classes.

Testing Exponentiality Against NBUL Alternatives Using Positive and Negative Fractional Moments

In this note a moment inequality for the New is Better than Used in Laplace ordering (NBUL) class of lifetime distributions is derived. A simple test statistic for testing exponentiality against NBUL alternatives is constructed. The test statistic is proved to be asymptotically normal and consistent. Critical values obtained by a Monte Carlo simulation are tabulated for different sample sizes. The asymptotic relative efficiency of the test is also studied.

A geometric process maintenance model with preventive repair

In this paper, a geometric process maintenance model with preventive repair is studied. A maintenance policy ( T, N) is applied by which the system will be repaired whenever it fails or its operating time reaches T whichever occurs first, and the system will be replaced by a new and identical one following the Nth failure. The long-run average cost per unit time is determined. An optimal policy ( T ∗, N ∗) could be determined numerically or analytically for minimizing the average cost. A new class of lifetime distribution which takes into account the effect of preventive repair is studied that is applied to determine the optimal policy ( T ∗, N ∗).

A Note on Classes of Lifetime Distributions

Some classes of lifetime distributions based on the failure rate are considered, namely new better than used failure rate (NBUFR), new better than average renewal failure rate (NBARFR) and generalized new better than average renewal failure rate (GNBARFR). Moment inequalities and moment generating functions of these classes under mixture and convolution are studied. In addition, the relationship between the scaled TTT-transform and the NBARFR class is investigated.

FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

PRESERVATIONS OF NBUC AND NBU(2) CLASSES UNDER MIXTURES

New integral inequality characterizations of the NBUC and NBU(2) classes of lifetime distributions are given. These results are then used to prove preservation under mixture results for the NBUC and NBU(2) classes.

Characterizations of classes of lifetime distributions generalizing the NBUE class

We introduce a new class of lifetime distributions exhibiting a notion of positive ageing, called the ℳ-class, which is strongly related to the well-known ℒ-class. It is shown that distributions in the ℳ-class cannot have an undesirable property recently observed in an example of an ℒ-class distribution by Klar (2002). Moreover, it is shown how these and related classes of life distributions can be characterized by expected remaining lifetimes after a family of random times, thus extending the notion of NBUE. We give examples of ℳ-class distributions by using simple sufficient conditions, and we derive reliability bounds for distributions in this class.