The Weibull-Geometric distribution

In this paper we introduce, for the first time, the Weibull-Geometric distribution which generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998). The hazard function of the last distribution is monotone decreasing but the hazard function of the new distribution can take more general forms. Unlike the Weibull distribution, the proposed distribution is useful for modeling unimodal failure rates. We derive the cumulative distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. We give expressions for the R\'enyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an algorithm EM (Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for estimating the parameters. We obtain the information matrix and discuss inference. Applications to real data sets are given to show the flexibility and potentiality of the proposed distribution

Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied

The Weibull-Exponential Distribution: Its Properties and Applications

A three parameter probability model, the so called Weibull-exponential distribution was proposed using the Weibull Generalized family of distributions. Some important models in the literature were found to be sub models of the new model. Explicit expressions for some of its basic mathematical properties like moments, moment generating function, reliability analysis, limiting behavior and order statistics were derived. The method of maximum likelihood estimation was proposed in estimating its parameters and real life applications were provided to illustrate its flexibility and potentiality over the exponential distribution

Oransal lindley fréchet dağılımının bazı teorik ve hesaplamalı yönleri

In this article, we study an extension of the Fréchet model by using the the odd Lindley-G family of distributions, which was introduced by [17]. Its some statistical properties such as quantile function, density shapes, moments, generating functions and order statistics are obtained. We estimate its parameters by maximum likelihood method. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood method. The usefulness of the odd Lindley Fréchet model is illustrated by means of three real data sets.Bu çalışmada, Fréchet modelinin genişletilmiş bir versiyonu [17] tarafından önerilen oransal Lindley dağılım ailesi kullanılarak çalışılmıştır. Bu modele ait kuantil fonksiyonu, yoğunluk biçimi, momentler, üreten fonksiyon ve sıra istatistikleri gibi istatistiksel özellikleri elde edilmiştir. Model parametrelerinin en çok olabilirlik tahminleri elde edildi. En çok olabilirlik parametre tahminleri için bir simülasyon çalışılması verilmiştir. Önerilen modelin gerçek veri seti üzerindeki uygunluğu için üç veri analizi yapılmıştır

Exponentiated Rama Distribution: Properties and Application

In this study, a new distribution known as the Exponentiated Rama distribution has been proposed. The aim was to generalize the one parameter Rama distribution using the exponentiation technique. Some properties of proposed distribution are derived. The maximum likelihood method was used for the estimation of model parameters. The proposed distribution was subjected to real life application using a set of lifetime data and compared to Rama distribution, Exponentiated Akash distribution and Exponentiated Exponential distribution and it was found to provide the best fit than other competing distributions. Keywords: Rama distribution, Exponentiated distributions, Order statistics, Moment

On Type II Half Logistic Weibull Distribution with Applications

In recent years, several of new improved and extended probability distributions have been discovered from the current distributions to facilitate their applications in many fields. A new three-parameter distribution, the so called the Type II half logistic Weibull (TIIHLW), is introduced for modeling lifetime data. Some mathematical properties of the TIIHLW distribution are provided. Explicit expressions for the moments, probability weighted moments, quantile function, order statistics and Rényi entropy are investigated. Maximum likelihood estimation technique is employed to estimate the model parameters and simulation issues are presented. In addition, the superiority of the subject distribution is illustrated with an application to two real data sets.  Indeed, the TIIHLW model yields a better fit to these data than the beta Weibull, Mcdonald Weibull and exponentiated Weibull distributions. Keywords: Type II half logistic-G class; Weibull distribution, Order statistics; Maximum likelihood method. DOI: 10.7176/MTM/9-1-0

Proposed X and S control charts for skewed distributions

This paper proposes a weighted variance method to compute the limits of the X and S charts for skewed distributions.The proposed charts extend the weighted variance X and R charts in by enabling a process from a skewed distribution with moderate and large sample sizes to be monitored efficiently, hence producing more favourable Type-I and Type-II error rates than the charts in.Note that the charts in are only intended to be used for small sample sizes. The Type-I and Type-II error rates computed show that the proposed charts outperform the existing heuristic charts, as well as those in for moderate and large sample sizes, involving cases with known and unknown parameters, when the distribution of a process is skewed

(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications and Extension

In this article, we introduce a new member of the Poisson-X family namely, the Poisson-exponentiated Weibull distribution. The statistical as well as the distributional properties of the new distribution are studied, and the performance of the maximum likelihood method of estimation is verified by a simulation study. The flexibility of the distribution is illustrated by a real data set. We develop and study a reliability test plan for the acceptance or rejection of a lot of products submitted for inspection when their lifetimes follow the new distribution. A real data example is also given to illustrate the feasibility of the sampling plan developed. Later, we introduce a bivariate analogue of the Poisson-exponentiated Weibull distribution called the Farlie-Gumbel-Morgenstern bivariate Poisson-exponentiated Weibull distribution and consider the concomitants of order statistics that arise from this bivariate distribution. The distribution theory of the concomitants of order statistics is also developed

The Transmuted Exponentiated Additive Weibull Distribution: Properties and Applications

A new generalization of the transmuted additive Weibull distribution is proposed by using the quadratic rank transmutation map, the so-called transmuted exponentiated additive Weibull distribution. It retains the characteristics of a good model. It is more flexible, being able to analyze more complex data; it includes twenty-seven sub-models as special cases and it is interpretable. Several mathematical properties of the new distribution as closed forms for ordinary and incomplete moments, quantiles, and moment generating function are presented, as well as the MLEs. The usefulness of the model is illustrated by using two real data sets