Class Of Lifetime Distributions Research Articles

Statistical inference of joint competing risks models from comparative bathtub shape distributions with hybrid censoring

In reliability engineering studies, the class of lifetime distributions with bathtub-shaped failure rate functions is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are frequently modelled with this characteristic. Comparative competing risk data are obtained in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we adopted the statistical inference of joint distributions with a bathtub shape or increasing failure rate function (Chen distributions). The problem of determining the relative merits of products according to their lifetime duration is discussed under the hybrid type-I censoring scheme. Also, under consideration of independent causes of failure, a survival analysis and the assessment of one risk in the presence of other risks are discussed. The maximum likelihood (ML) method and the Bayes approach relative to the symmetric loss function are used to estimate the model parameters. Additionally, we build the classical confidence intervals (CIs) (asymptotic CI and bootstrap CI) to compare with the Bayes credible intervals. Moreover, theoretical results are evaluated and contrasted using a Monte Carlo simulation study. Finally, for illustration purposes, a real data set obtained from a laboratory experiment is evaluated using the suggested model with some brief comments.

A New Two-Sided Class of Lifetime Distributions: Applications to Complete and Right Censored Data

In this article, we first define a new two-sided distribution called the two-sided Kumaraswamy distribution and then we propose a generalized class of lifetime distributions via compounding two-sided Kumaraswamy and a baseline distribution. One of the advantages of this class of new distributions is that they can be unimodal or bimodal. The general model is specified by taking the exponential distribution as the baseline distribution. Some basic properties of the proposed distribution are derived. The model parameters are estimated by means of maximum likelihood method. In addition, parametric and non-parametric bootstrap procedures are used to obtain point estimates and confidence intervals of the parameters of the model. A simulation study has been conducted to examine the bias and the mean square error of the maximum likelihood estimators. We illustrate the performance of the proposed distribution by means of two real data sets (one is complete data set and other is right censored data set) and both the data sets show that the new distribution is more appropriate as compared to Weibull, gamma, weighted exponential, generalized two-sided exponential, generalized transmuted two-sided exponential and generalized exponential distributions.

Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures

This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.

The Odd Log-Logistic Transmuted-G Family of Distributions: Properties, Characterization, Applications and Different Methods of Estimation

In this work, we propose a new class of lifetime distributions called the odd log-logistic transmuted-G family. The proposed family of distributions is constructed by compounding the odd log-logistic distribution with the transmuted distribution. It can provide better fits than some of the known lifetime models and this fact represents a good characterization of this new family. Some characterizations for the new family are presented as well as some of its mathematical properties including. The maximum likelihood, Least squares and weighted least squares, Cram\'{e}r--von--Mises, Anderson-Darling and right-tailed Anderson-Darlingare and maximum product of spacings methods are used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application to a real data set.

A new class of distributions on the whole real line based on the continuous iteration approach

The continuous iteration of an exponential-type function allows to describe a whole range of growths between logarithmical and exponential. This principle has been applied to a class of lifetime distributions called Tetration distribution and its subsequent tail has the property to belong to an extremely versatile family, from heavy-tailed to light-tailed. The present paper aims to construct a statistical distribution on the whole real line, based on the same principle. This new distribution, denoted Asymmetric Tetration distribution is obtained by combining a reflection of the Tetration distribution with skewing methods. Two inference methods are developed and compared in terms of performance of their estimators. In addition, an index of tail heaviness at is proposed and computed for the most common distributions on the whole real line. Finally, the Asymmetric Tetration distribution is applied to data sets in the finance domain.

Testing brnbu ageing class of life-time distribution based on moment inequality

In this paper, new moment inequality is derived for Bivariate Renewal New Better than Used (BRNBU) ageing class of life-time distribution. This inequality demonstrates that if the mean life is finite, then all higher order moments exist. Based on the Moment inequality, new testing procedures for testing bivariate exponentiality against BRNBU ageing class of life-time distribution is introduced.The asymptotic normality of the test statistic and its consistency are studied. Using Monte Carlo Method, critical values of the proposed test are calculated for n= 5(5)100 and tabulated. Finally, the theoretical results are applied to analyze real-life data sets.

A new class of lifetime distribution with decreasing failure rate: Properties and applications

The exponential model is the simplest among all lifetime distribution models and it possesses a constant failure rate. Here we propose a new class of lifetime distribution having decreasing failure rate which we developed through compounding exponential distribution with the positive hyper-Poisson distribution. We investigate some of its statistical properties and employed various methods of estimation for estimating the parameters of the distribution along with certain test procedures. All the procedures discussed in the paper are illustrated with the help of real-life data sets. Further, a brief simulation study is conducted for examining the performance of the estimators of the parameters of the distribution.

Some new results on bathtub-shaped hazard rate models.

The most common non-monotonic hazard rate situations in life sciences and engineering involves bathtub shapes. This paper focuses on the quantile residual life function in the class of lifetime distributions that have bathtub-shaped hazard rate functions. For this class of distributions, the shape of the α-quantile residual lifetime function was studied. Then, the change points of the α-quantile residual life function of a general weighted hazard rate model were compared with the corresponding change points of the basic model in terms of their location. As a special weighted model, the order statistics were considered and the change points related to the order statistics were compared with the change points of the baseline distribution. Moreover, some comparisons of the change points of two different order statistics were presented.

Shock models leading to G* class of lifetime distributions

In this paper we study a stochastic ordering namely alternate probability generating function (a.p.g.f .... ) ordering and its properties. The life distribution H(t) of a device subject to shocks governed by a Poisson process is considered as a function of the probabilities Pk of surviving the first k shocks. Various properties of the discrete failure distribution Pk are shown to be reflected in corresponding properties of the continuous life distribution H(t). A certain cumulative damage model and various applications of these models in reliability modeling are also considered.

Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function

AbstractA new class of lifetime distributions, called tetration distribution, is presented based on the continuous iteration of the exponential‐minus‐one function. In particular, this distribution encompasses and extends the Weibull, Pareto, and Gompertz distributions. In addition, a characterization of the tail of the distribution is proposed through two indices, one of them encompassing the Pareto and Weibull tail indices. Finally, an inference procedure based on rank regression is implemented for the tetration distribution and applied to multiple datasets from the reliability field.

Exponentiated Rayleigh Poisson Distribution: Model, Properties and Applications

In this research paper, a new class of life-time distribution is introduced by compounding A new generalization of Rayleigh distribution; properties and applications and The Exponentiated G Poisson model, the so-called Exponentiated Rayleigh Poisson distribution. Main aim of this research article is to enhance the flexibility of Exponentiated G. Poisson distribution by power transformation technique. The probability density function, the survival function and the hazard function of the new proposed model in graphical form are illustrated. We study the properties of this new distribution with special emphasis on its quantile function, mode, skewness, kurtosis and moments. We have discussed residual life function, the probability-weighted moments, order statistics, R'enyi and entropies. We also discussed parameter estimation considering the maximum likelihood estimation approach. We have calculated the value of log-likelihood, Akaike's information criteria, Bayesian information criteria, corrected Akaike's information criteria and Hennan-Quinn information criteria of Generalized Rayleigh distribution, Exponentiated Chen distribution, Exponentiated Exponential distribution, Exponentiated Inverted Weibull distribution, Compound Rayleigh distribution and newly proposed Exponentiated Rayleigh Poisson distribution and found that the newly proposed model has smaller values in comparison to other. We have studied the P-P plot, Q-Q plot Kolmogorov Smirnov test and TTT plot of the proposed distribution for model validation. We compared the empirical distribution CDF and estimated distributed function CDF of the proposed model with five other models. A real dataset is analyzed for illustrative purposes. The importance and flexibility of the new family is illustrated by applying different techniques and tools. A final conclusion concludes the paper.

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

AbstractWe consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.

On shift-dependent generalized entropies for doubly truncated random variable

Recently, Das (2017) studied the importance of weighted generalized entropy for one sided truncation problems. There are some situations in survival study, where data are usually truncated from both sides. In such cases, individuals whose event-time lies within a certain time interval are only observed. The concept of first kind as well as second kind weighted doubly truncated generalized entropy measures is studied in this paper. It is showed that they characterize the distribution function uniquely. Further, the effect of monotone transformations on these measures is discussed. Uncertainty orders and its relation with the usual stochastic order are presented. Nonparametric class of lifetime distributions is introduced and some inequalities are obtained. Various examples are provided for illustration purpose.

A New Class of Power Function Distribution: Properties and Applications

A new class of lifetime distributions called the power function power series (PFPS) is introduced. This new class is obtained by compounding power function and power series distributions. Structural properties of PFPS class are studied, including; quantile function, order statistics, moments, Bonferroni and Lorenz curves, probability weighted moments, mean residual life and entropy measure. Two sub-models in the new class of PFPS are provided. Maximum likelihood method is employed to obtain parameter estimator of the class. Analysis of two real data sets is conducted to demonstrate the usefulness of two sub-models from the new class.

A Three Parameter Generalized Lindley Distribution: Properties and Application

In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study.

New nonparametric classes of distributions in terms of mean time to failure in age replacement

Abstract The mean time to failure (MTTF) function in age replacement is used to evaluate the performance and effectiveness of the age replacement policy. In this paper, based on the MTTF function, we introduce two new nonparametric classes of lifetime distributions with nonmonotonic mean time to failure in age replacement; increasing then decreasing MTTF (IDMTTF) and decreasing then increasing MTTF (DIMTTF). The implications between these classes of distributions and some existing classes of nonmonotonic ageing classes are studied. The characterizations of IDMTTF and DIMTTF in terms of the scaled total time on test transform are also obtained.

The Generalized Odd Weibull Generated Family of Distributions:Statistical Properties and Applications

In this work, we propose a new class of lifetime distributions calledthe generalized odd Weibull generatedfamily. It can provide better fits than some of the well known lifetime models and this fact represents a good characterization of this family. Some of its mathematical properties are derived. The maximum likelihood method is used for estimating the model parameters. We study the behaviour of the estimators by means of two Monte Carlo simulations. The importance of the family illustrated by means of two applications to real data sets.

Exponentiated Power Lindley Logarithmic: Model, Properties and Applications

A new class of lifetime distributions is proposed. Closed form expressions are provided for the density, cumulative distribution, survival and hazard rate functions. Maximum likelihood estimation is discussed and formulas for the elements of the observed information matrix are provided. Simulation studies are conducted. Finally, two real data applications are given showing the flexibility and potentiality of the new distribution

On Log-Inverse Weibull Distribution and Its Properties

SYNOPTIC ABSTRACTIn this article, we consider a wide class of life time distributions; namely, the log-inverse Weibull distribution and investigate some of its important theoretical properties. We obtain a location-scale extension of the distribution and discuss the estimation of its parameters by method of maximum likelihood. We have fitted the proposed models to certain real life data sets for illustrating their usefullness, and have conducted a brief simulation study for examining the performance of the maximum likelihood estimators of the parameters of the distribution.

A new lifetime model with different types of failure rate

ABSTRACTA new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.