New Class Of Lifetime Distributions Research Articles

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.

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.

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.

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

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.

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.

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

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.

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.