Power Series Family Of Distributions Research Articles

Exponentiated Complementary Kumaraswamy-G Power Series Family of Distributions with Application to Lifetime Data

This paper proposed the Exponentiated Complementary Kumaraswamy - G Power (ECK-GP) Series family of distributions which is an extension of the Complementary Kumaraswamy-G Power Series family of distributions. The expressions for its densities, basic statistical properties and parameters estimation using the method of Maximum Likelihood were derived and established. An application of the Exponentiated Complementary Kumaraswamy Exponential Poisson (ECKEP) distribution to a real lifetime dataset clearly reveals its suitability and flexibility in fitting real life dataset.

Power Series Generalised Power Weibull Class of Distributions

The power series generalised power Weibull class of distributions were developed in this study by compounding the power series family of distributions and the generalised power Weibull distribution. The statistical properties of this new class were derived. Maximum likelihood parameter estimators were derived for the parameters of the power series generalised power Weibull class of distributions. Four sub-families of distributions were developed from the power series generalised power Weibull class of distribution; the generalised power Weibull geometric distribution, generalised power Weibull Poisson distribution, generalised power Weibull binomial distribution and the generalised power Weibull logarithmic distribution. The hazard rate and probability density function plots of the four sub families of distributions showed that, they can model both monotonic and non-monotonic lifetime data. Monte Carlo simulations performed on these sub-distributions showed that, their estimators were consistent estimators. Application of these sub-distributions to failure data from air conditioning system of an aircraft showed that, the generalised power Weibull geometric distribution provides a better fit to the data. Also, the generalised power Weibull Poisson distribution provides a better fit to the data on service times of 63 aircraft.

Modeling rounded counts using a zero-inflated mixture of power series family of distributions.

This paper proposes an extension of zero-inflated models for analyzing rounded counting outcomes. A zero-inflated mixture of power series is proposed, and the EM algorithm is developed to estimate parameters. The accuracy of estimators is evaluated using a simulation study. The results of simulations show that the estimation procedure is successful and estimates are accurate. An application of our models for analyzing the number of cigarettes smoked per day of respondents for the American's Changing Lives study is enclosed. The proposed model best fits the data and the relationships between rounded counts and other covariates revealed by proposed regression models.

Generalized extended Weibull power series family of distributions

In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.

The odd Weibull-Topp-Leone-G power series family of distributions: model, properties, and applications

A new generalization of the odd Weibull-Topp-Leone-G family of distributions called the odd Weibull-Topp-Leone-G power series family of distributions is developed. Statistical properties of the new distribution were derived. We also derive the maximum likelihood estimates of the proposed model. Some special cases for the new family of distributions were also considered. We conducted a simulation study to evaluate the consistency of the maximum likelihood estimates. Two real data examples were also considered to demonstrate the usefulness of the newly proposed family of distributions.

Correction* Exponentiated quasi power Lindley power series distribution with applications in medical science

Abstract The present paper introduces an advanced five parameter lifetime model which is obtained by compounding exponentiated quasi power Lindley distribution with power series family of distributions. The EQPLPS family of distributions contains several lifetime sub-classes such as quasi power Lindley power series, power Lindley power series, quasi Lindley power series and Lindley power series. The proposed distribution exhibits decreasing, increasing and bathtub shaped hazard rate functions depending on its parameters. It is more flexible as it can generate new lifetime distributions as well as some existing distributions. Various statistical properties including closed form expressions for density function, cumulative function, limiting behaviour, moment generating function and moments of order statistics are brought forefront. The capability of the quantile measures in terms of Lambert W function is also discussed. Ultimately, the potentiality and the flexibility of the new class of distributions has been demonstrated by taking three real life data sets by comparing its sub-models.

Pair copula construction for longitudinal data with zero-inflated power series marginal distributions

ABSTRACT Assessing the temporal dependency among outcomes under investigation is critical in many fields. One complication in the modeling process of the discrete longitudinal data is the presence of excess zeros. We propose a framework for modeling count repeated measurements using members of power series family of distributions. The framework accommodates count outcomes having extra zeros. The longitudinal observations of response variable is modeled using pair copula constructions with a D-vine structure. The maximum likelihood estimates of parameters are obtained using a two-stage approach. Some simulation studies are performed for illustration of the proposed methods, for comparing its performance with that of a generalized linear mixed effects (GLME) model and for assessing the robustness of D-vine and GLME models with respect to the distribution of random effects. In the empirical analysis, the proposed method is applied for analysing a real data set of a kidney allograft rejection study.

Exponentiated quasi power Lindley power series distribution with applications in medical science

Abstract The present paper introduces an advanced five parameter lifetime model which is obtained by compounding exponentiated quasi power Lindley distribution with power series family of distributions. The EQPLPS family of distributions contains several lifetime sub-classes such as quasi power Lindley power series, power Lindley power series, quasi Lindley power series and Lindley power series. The proposed distribution exhibits decreasing, increasing and bathtub shaped hazard rate functions depending on its parameters. It is more flexible as it can generate new lifetime distributions as well as some existing distributions. Various statistical properties including closed form expressions for density function, cumulative function, limiting behaviour, moment generating function and moments of order statistics are brought forefront. The capability of the quantile measures in terms of Lambert W function is also discussed. Ultimately, the potentiality and the flexibility of the new class of distributions has been demonstrated by taking three real life data sets by comparing its sub-models.

Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications.

In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

Gaussian copula joint models to analysis mixed correlated longitudinal count and continuous responses

Gaussian Copula joint models for analyzing mixed correlated longitudinal continuous and count responses with random effects are presented where the count response is defined by a latent variable approach, and its distribution is a member of the power series family of distributions. A copula-based joint model is proposed that accounts for associations between count and continuous responses. A full likelihood-based inference method for estimation is used by which maximum likelihood estimation of parameters is obtained. To illustrate the utility of the models, some simulation studies are performed. Finally, the proposed models are motivated by analyzing a medical data set where the correlated responses are the number of joint damaged obtained from the severity of osteoporosis (count response) and Body Mass Index (continuous response). Effects of some covariates on responses are investigated simultaneously. Besides, identifiability of parameters, detection of outlines by examining residuals and sensitivity analyses are fully investigated.

Multivariate power series interpoint distances

We establish (a) the probability mass function of the interpoint distance (IPD) between random vectors that are drawn from the multivariate power series family of distributions (MPSD); (b) obtain the distribution of the IPD within one sample and across two samples from this family; (c) determine the distribution of the MPSD Euclidean norm and distance from fixed points in $${\mathbb {Z}}^d$$ ; and (d) provide the distribution of the IPDs of vectors drawn from a mixture of the MPSD distributions. We present a method for testing the homogeneity of MPSD mixtures using the sample IPDs.

On estimating reliability function for the family of power series distribution

Explicit expression of the Stress - Strength reliability function, is derived, when the stress (X) and strength (Y) distributions are different members of the Power series family of distributions. Minimum Variance Unbiased (MVU) estimator of R, variance of the MVU estimator together with its MVU estimator are derived for Power series family of distributions. Maximum Likelihood (ML) estimator of R along with related large sample results are also derived. Analytic expressions of the above mentioned quantities are provided for different members of the Power series family of distributions. Further, an application, in the context of real Soccer games, is enumerated.

On the use of the modified power series family of distributions in a cure rate model context.

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the Expectation Maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented.

The Odd Log-Logistic Power Series Family of Distributions: Properties and Applications

A new family of continuous distributions obtained by compounding the odd log-logistic and power series distributions is introduced. The mathematical properties of the proposed family are discussed. The estimation of the parameters is considered by the maximum likelihood method. In order to assess the finite sample performance of maximum likelihood estimators, simulation studies are performed. Finally, the potentiality of the family is illustrated by means of applications to two real data sets.

Exponentiated Generalized Power Series Family of Distributions

In this paper, a new family of distributions called the exponentiated generalized power series family is proposed and studied. Statistical properties such as stochastic order, quantile function, entropy, mean residual life and order statistics were derived. Bivariate and multivariate extensions of the family was proposed. The method of maximum likelihood estimation was proposed for the estimation of the parameters. Some special distributions from the family were defined and their applications were demonstrated with real data sets.

Inference for Zero Inflated Truncated Power Series Family of Distributions

Inference for Zero Inflated Truncated Power Series Family of Distributions

The Complementary Exponentiated Inverted Weibull Power Series Family of Distributions and its Applications

DOI: 10.9734/BJMCS/2016/21903 Editor(s): (1) H. M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Canada. Reviewers: (1) G. Y. Sheu, Chang-Jung Christian University, Tainan, Taiwan. (2) P. E. Oguntunde, Covenant University, Nigeria. (3) Thomas L. Toulias, Technological Educational Institute of Athens, Greece. Complete Peer review History: http://sciencedomain.org/review-history/12518

Generalizedextended Weibull Power Series Family of Distributions

Generalizedextended Weibull Power Series Family of Distributions

Parametric Bayesian inference for Y-linked two-sex branching models

A Y-linked two-sex branching process with blind choice is a suitable model for analyzing the evolution of the number of carriers of two alleles of a Y-linked gene in a two-sex monogamous population where each female chooses her partner from among the male population without caring about his type (i.e., the allele he carries). This work focuses on the development of Bayesian inference for this model, considering a parametric framework with the reproduction laws belonging to the power series family of distributions. A sample is considered given by the observation of the total number of females and males (regardless of their types) up to some generation as well as the number of each type of male in the last generation. Using a simulation method based on the Gibbs sampler, we approximate the posterior distributions of the main parameters of this model. The accuracy of the procedure based on this sample is illustrated by way of a simulated example.