Showing papers on "Natural exponential family published in 2016"
TL;DR: In this paper, the Topp-Leone family of distributions is proposed and general expression for density and distribution function of the new family is given. But the proposed family is not suitable for the case of large numbers of nodes.
Abstract: In this paper we have proposed a new family of distributions; the Topp–Leone family of distributions. We have given general expression for density and distribution function of the new family. Expression for moments and hazard rate has also been given. We have also given an example of the proposed family.
81 citations
TL;DR: A simple and effective simulator of the strong-turbulence FSO channel that addresses the influence of the temporal covariance effect and provides K and gamma-gamma distributed values with the exponential autocorrelation function and a prescribed correlation time is proposed.
Abstract: The simulation of a free-space optical (FSO) communication channel in the presence of strong turbulence typically requires the generation of channel states with a K or gamma–gamma distribution and a predefined autocorrelation function. In this paper, we propose a simple and effective simulator of the strong-turbulence FSO channel that addresses the influence of the temporal covariance effect. Specifically, the proposed simulator provides K and gamma–gamma distributed values with the exponential autocorrelation function and a prescribed correlation time. This simulator is based on the numerical solution of the first-order stochastic differential equation. The simulated channel states are generated by a simple discrete-time differential equation and the simulator performance is analyzed in the paper.
36 citations
TL;DR: In this article, a family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y] framework, which is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Frechet distributions.
Abstract: A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Frechet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entropy. Some members of the T-Cauchy{Y} family are developed and one member, gamma-Cauchy{exponential} distribution, is studied in detail. The distributions in the T-Cauchy{Y} family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right or skewed to the left.
34 citations
Journal Article•
TL;DR: In this paper, the authors introduced a new family of continuous distributions called a Garhy generated family of distributions and derived explicit expressions for the quantile function, ordinary and incomplete moments, generating function and order statistics.
Abstract: This paper introduces a new family of continuous distributions called a Garhy generated family of distributions. Some mathematical properties of this family are discussed. The derived properties are hold to any proper distribution in this family. Some special sub-models in the new family are derived. General explicit expressions for the quantile function, ordinary and incomplete moments, generating function and order statistics are obtained. The estimation of the model parameters is discussed by using maximum likelihood and the potentiality of the extended family is illustrated with one application to real data. Keywords : Kumaraswamy distribution; Exponetiated distribution; Moments; quantile function, Maximum likelihood estimation.
28 citations
TL;DR: This work provides a computational strategy for deriving the explicit expression of the Laurent polynomial sequence that identifies the family of exponential pseudo-splines, the nonstationary counterpart of (polynomial) pseudo- splines and includes exponential B-spline as a special subclass.
27 citations
TL;DR: This paper introduces two new families of multivariate distributions with finite or infinite support above or below the diagonal generated by McKay's bivariate gamma distribution and shows that their conditional distributions are univariate gamma- and beta-generated distributions.
26 citations
TL;DR: A new family of Marshall-Olkin extended generalized linear exponential distribution is introduced that has the advantage of being capable of modeling various shapes of aging and failure criteria and provides a better fit than some other known distributions.
23 citations
TL;DR: A class of semi-parametric/parametric shrinkage estimators are introduced and their asymptotic optimality properties are established, and the simultaneous inference of mean parameters in a family of distributions with quadratic variance function is discussed.
Abstract: This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
21 citations
11 Feb 2016
TL;DR: In this article, a convolution of generated random variable from independent and identically exponential distribution with stabilizer constant is constructed and the characteristic function of this distribution is obtained by using Laplace-Stieltjes transform.
Abstract: It is constructed convolution of generated random variable from independent and identically exponential distribution with stabilizer constant. The characteristic function of this distribution is obtained by using Laplace-Stieltjes transform. The uniform continuity property of characteristic function from this convolution is obtained by using analytical methods as basic properties.
20 citations
TL;DR: In this article, the authors studied general mathematical properties of the Poisson-X family in the context of the T -X family of distributions pioneered by Alzaatreh et al. which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy.
Abstract: Recently, Ristic and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down ba...
19 citations
TL;DR: A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model where the defective density function associated to the ruin probability is projected in an orthogonal polynomial system.
TL;DR: The exponentiated Marshal-Olkin family of distributions as discussed by the authors is a family of continuous distributions with three extra shape parameters, and it has been shown empirically the potential of the family by means of two applications to real data.
Abstract: We study general mathematical properties of a new class of continuous distributions with three extra shape parameters called the exponentiated Marshal-Olkin family of distributions. Further, we present some special models of the new class and investigate the shapes and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions and probability weighted moments. We discuss the estimation of the model parameters by maximum likelihood and show empirically the potentiality of the family by means of two applications to real data.
TL;DR: In this paper, a new family of distributions called the Poisson-odd generalized exponential distribution (POGE) was introduced, which has the odd generalized exponential as its limiting distribution.
Abstract: In this paper, we introduce a new family of distributions called the Poisson-odd generalized exponential distribution (POGE). Various properties of the new model are derived and studied. The new distribution has the odd generalized exponential as its limiting distribution. We present and study two special cases of the POGE family of distributions, namely the Poisson odd generalized exponential-half logistic and the Poisson odd generalized exponential-uniform distributions. Estimation and inference procedure for the parameters of the new distribution are discussed by the method of maximum likelihood; we also evaluate the proposed estimation method by simulation studies. Applications to two real data sets are provided in order to demonstrate the performance of the proposed family of distributions.
TL;DR: In this paper, a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution is proposed. But the proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-poisson distributions.
Abstract: This paper introduces a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution. Many well-known distributions are particular and limiting distributions. The proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-Poisson distributions. Probability and moment recurrence formulae, and probabilistic and reliability properties have been derived. With the flexibility to model under-, equi- and over-dispersion, and its various interesting properties, this NB generalization will be a useful model for count data. An application to empirical modeling is illustrated with a real data set.
TL;DR: This paper introduced a skewness parameter into Vaughan's (2002) generalized secant hyperbolic distribution by means of exponential tilting and developed some properties of the new distribution family.
Abstract: We introduce a skewness parameter into Vaughan’s (2002) generalized secant hyperbolic (GSH) distribution by means of exponential tilting and develop some properties of the new distribution family. In particular, the moment-generating function is derived which ensures the existence of all moments. Finally, the flexibility of our distribution is compared to similar parametric models by means of moment-ratio plots and application to foreign exchange rate data.
Journal Article•
TL;DR: In this paper, a new family of distributions called Kumaraswamy-generalized power Weibull (Kgpw) distribution is proposed and studied, which has a number of well known sub-models such as Weibbull, exponentiated Weibell, Kumar aswamy Weibler, generalized power Weibrler, and new sub-model, namely, generalized generalized power exponential distributions.
Abstract: A new family of distributions called Kumaraswamy-generalized power Weibull (Kgpw) distribution is proposed and studied. This family has a number of well known sub-models such as Weibull, exponentiated Weibull, Kumaraswamy Weibull, generalized power Weibull and new sub-models, namely, exponentiated generalized power Weibull, Kumaraswamy generalized power exponential distributions. Some statistical properties of the new distribution include its moments, moment generating function, quantile function and hazard function are derived. In addition, maximum likelihood estimates of the model parameters are obtained. An application as well as comparisons of the Kgpw and its sub-distributions is given. Keywords: Generalized power Weibull distribution, Kumaraswamy distribution, Maximum likelihood estimation, Moment generating function, Hazard rate function.
TL;DR: In this paper, a comparative study of two-parameter gamma and Weibull distributions for modeling lifetime data from various fields of knowledge is presented, where the authors compare the goodness of fit of the two distributions for lifetime data.
Abstract: The analysis and modeling of lifetime data are crucial in almost all applied sciences including medicine, insurance, engineering, behavioral sciences and finance, amongst others. The main objective of this paper is to have a comparative study of two-parameter gamma and Weibull distributions for modeling lifetime data from various fields of knowledge. Since exponential distribution is a particular case of both gamma and Weibull distributions and the exponential distribution is a classical distribution for modeling lifetime data, the goodness of fit of both gamma and Weibull distributions are compared with exponential distribution.
TL;DR: In this article, a two-parameter lifetime distribution obtained by compounding the generalized exponential and exponential distributions was proposed, where the shape parameter of the GED was assumed to be a random variable having the exponential distribution.
Abstract: We introduce a new two-parameter lifetime distribution obtained by compounding the generalized exponential and exponential distributions. We assume that the shape parameter of the generalized exponential distribution is a random variable having the exponential distribution. The shapes of the density and hazard rate functions are derived. The model parameters are estimated by maximum likelihood, and an application of the proposed distribution is presented.
01 Jan 2016
TL;DR: The characteristics of PH and ME distributions are dealt with, and their use in stochastic analysis of complex systems is revised.
Abstract: Since their introduction, properties of Phase Type (PH) distributions have been analyzed and many interesting theoretical results found. Thanks to these results, PH distributions have been profitably used in many modeling contexts where non-exponentially distributed behavior is present. Matrix Exponential (ME) distributions are distributions whose matrix representation is structurally similar to that of PH distributions but represent a larger class. For this reason, ME distributions can be usefully employed in modeling contexts in place of PH distributions using the same computational techniques and similar algorithms, giving rise to new opportunities. They are able to represent different dynamics, e.g., faster dynamics, or the same dynamics but at lower computational cost. In this chapter, we deal with the characteristics of PH and ME distributions, and their use in stochastic analysis of complex systems. Moreover, the techniques used in the analysis to take advantage of them are revised.
Journal Article•
TL;DR: In this paper, the hyperbolic cosine exponential (HCF) distribution with two parameters is introduced and its properties are explored, including the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics, stress-strength parameter and expression of the Shannon entropy.
Abstract: A new class of distributions called the hyperbolic cosine – F (HCF) distribution is introduced and its properties are explored.This new class of distributions is obtained by compounding a baseline F distribution with the hyperbolic cosine function. This technique resulted in adding an extra parameter to a family of distributions for more flexibility. A special case with two parameters has been considered in details namely; hyperbolic cosine exponential (HCE) distribution. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics, stress-strength parameter and expression of the Shannon entropy are derived. Estimations of parameters in HCE distribution for two data sets obtained by eight estimation procedures: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. Finally these data sets have been analyzed for illustrative purposes and it is observed that in both cases the proposed model fits better than Weibull, gamma and generalized exponentialdistributions.
TL;DR: In this paper, the authors introduced Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al. They derived the shape properties of density function and hazard function.
Abstract: Nadarajah et al.(2013) introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al.(2013). The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011).
TL;DR: In this paper, the exponential Weibull distribution is introduced for analyzing positive data and the parameters of the proposed distribution are estimated by making use of the maximum likelihood approach, where the density function is utilized to model two actual data sets.
Abstract: exponentiated exponential Weibull distribution is being introduced in this paper. The new model turns out to be quite exible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson-Darling and Cramer-von Mises goodness-of-fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various elds of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.
TL;DR: In this paper, the normal inverse Gaussian distributions are used to introduce the class of multivariate normal α-stable distributions, and the expression of the variance function of the generated natural exponential family is given.
Abstract: The normal inverse Gaussian distributions are used to introduce the class of multivariate normal α-stable distributions. Some fundamental properties of these new distributions are established. We give the expression of the variance function of the generated natural exponential family and we use the Levy–Khintchine representation to determine the associated Levy measure. We also study the relationship between these distributions and the multivariate inverse Gaussian ones.
TL;DR: In this paper, the simultaneous inference of mean parameters in a family of distributions with quadratic variance function is discussed, and a class of semiparametric/parametric shrinkage estimators and their asymptotic optimality properties are established.
Abstract: This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semiparametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
TL;DR: In this paper, a two-parameter weighted exponential distribution which has more mild algebraic properties than the existing weighted exponential distributions was studied and explicit expressions for some of its basic statistical properties including moments, reliability analysis, quantile function and order statistics were derived.
Abstract: A new two-parameter weighted exponential distribution which has more mild algebraic properties than the existing weighted exponential distribution was studied. Explicit expressions for some of its basic statistical properties including moments, reliability analysis, quantile function and order statistics were derived. Its parameters were estimated using the method of maximum likelihood estimation. The new probability model was applied to four real data sets to assess its flexibility over the existing weighted exponential distribution.
TL;DR: A new four-parameter family of distributions is proposed by compounding the generalized gamma and power series distributions by using the compounding procedure based on the work by Marshall and Olkin (1997) and defines 76 sub-models.
TL;DR: In this article, the gamma-generated family of distributions with an extra positive shape parameter is studied and some properties of the family are examined. But the authors did not consider the properties of these distributions for any baseline model.
Abstract: Adding new shape parameters to expand a model into a larger family of distributions to provide significantly skewed and heavy-tails plays a fundamental role in distribution theory. For any continuous baseline G distribution, Ristic and Balakrishnan (2012) proposed the gamma-generated family of distributions with an extra positive shape parameter. They presented some special models of their family but did not study its properties. This paper examines some general mathematical properties of this family which hold for any baseline model. Some distributions are studied and a number of existing results in the literature can be recovered as special cases. We estimate the model parameters by maximum likelihood and illustrate the importance of the family by means of an application to a real data set.
05 Oct 2016
TL;DR: It is shown that for the first non-trivial order, which is order 3, the \(\hbox {cv}\) cannot be less than 0.200902 but the proof of this conjecture is still missing.
Abstract: We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (\(\hbox {cv}\)). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the \(\hbox {cv}\) cannot be less than 0.200902 but the proof of this conjecture is still missing.
TL;DR: In this paper, two extensions of the Exponential model to describe income distributions are proposed and applied to study the distribution of incomes in Australia for the period 2001-2012, and they find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.
Abstract: In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT–Lognormal models discussed in this paper preserve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT–Lognormal models to study the distribution of incomes in Australia for the period 2001–2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.
18 May 2016
TL;DR: In this article, the authors consider the reliability properties of the weighted exponential distribution proposed by Gupta and Kundu (2009) and discuss its various reliability properties and discuss different properties and inferential issues.
Abstract: In this paper we consider the weighted exponential distribution proposed by Gupta and Kundu (Statistics 43:621–634, 2009) and discuss its various reliability properties. We further consider the length biased version of the weighted exponential distribution, and discuss different properties and inferential issues. The maximum likelihood estimators of the unknown parameters of the proposed length biased weighted exponential distribution has been addressed. One data set has been analyzed for illustrative purposes.