Showing papers on "Kumaraswamy distribution published in 2013"
TL;DR: In this article, the authors proposed a generalization of the Kumaraswamy distribution, referred to as the exponentiated KG distribution, and derived the moments, moment generating function, mean deviations, Bonferroni and Lorentz curves, density of the order statistics and their moments.
Abstract: The paper by Kumaraswamy (Journal of Hydrology 46 (1980) 79–88) introduced a probability distribution for double bounded random processes which has considerable attention in hydrology and related areas. Based on this distribution, we propose a generalization of the Kumaraswamy distribution refereed to as the exponentiated Kumaraswamy distribution. We derive the moments, moment generating function, mean deviations, Bonferroni and Lorentz curves, density of the order statistics and their moments. We also present a related distribution, so-called the log-exponentiated Kumaraswamy distribution, which extends the generalized exponential (Aust. N. Z. J. Stat. 41 (1999) 173–188) and double generalized exponential (J. Stat. Comput. Simul. 80 (2010) 159–172) distributions. We discuss maximum likelihood estimation of the model parameters. In applications to real data sets, we show that the log-exponentiated Kumaraswamy model can be used quite effectively in analyzing lifetime data.
95 citations
TL;DR: In this paper, a five-parameter Kumaraswamy Burr XII (KwBXII) distribution is defined and studied, which contains some well-known distributions discussed in lifetime literature, such as the logistic, Weibull and Burr XII distributions.
Abstract: For the first time, a five-parameter distribution, called the Kumaraswamy Burr XII (KwBXII) distribution, is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the logistic, Weibull and Burr XII distributions, among several others. We obtain the complete moments, incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and reliability of the KwBXII distribution. We provide two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the KwBXII distribution. Three applications to real data sets demonstrate the usefulness of the proposed distribution and that it may attract wider applications in lifetime data analysis.
91 citations
01 Feb 2013
TL;DR: In this article, two median-dispersion re-parameterizations of the Kumaraswamy distribution are presented to facilitate its use in regression models in which both the location and the dispersion parameters are functions of their own distinct sets of covariates.
Abstract: The Kumaraswamy distribution is very similar to the Beta distribution, but has the important advantage of an invertible closed form cumulative distribution function. The parameterization of the distribution in terms of shape parameters and the lack of simple expressions for its mean and variance hinder, however, its utilization with modeling purposes. The paper presents two median-dispersion re-parameterizations of the Kumaraswamy distribution aimed at facilitating its use in regression models in which both the location and the dispersion parameters are functions of their own distinct sets of covariates, and in latent-variable and other models estimated through simulation-based methods. In both re-parameterizations the dispersion parameter establishes a quantile-spread order among Kumaraswamy distributions with the same median and support. The study also describes the behavior of the re-parameterized distributions, determines some of their limiting distributions, and discusses the potential comparative advantages of using them in the context of regression modeling and simulation-based estimation.
57 citations
TL;DR: The Kumaraswamy Pareto distribution, for the first time, is introduced and studied and can have a decreasing and upside-down bathtub failure rate function depending on the values of its parameters.
Abstract: The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on the values of its parameters. It includes as special sub-models the Pareto and exponentiated Pareto (Gupta et al., 1998) distributions. Some structural properties of the proposed distribution are studied including explicit expressions for the moments and generating function. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with widely known distributions.
53 citations
TL;DR: In this paper, a bivariate Kumaraswamy (BVK) distribution with absolute continuous and singular parts is proposed. And the cumulative distribution function of this bivariate model has absolutely continuous and single parts.
Abstract: In this paper, we introduce a bivariate Kumaraswamy (BVK) distribution whose marginals are Kumaraswamy distributions. The cumulative distribution function of this bivariate model has absolutely continuous and singular parts. Representations for the cumulative and density functions are presented and properties such as marginal and conditional distributions, product moments and conditional moments are obtained. We show that the BVK model can be obtained from the Marshall and Olkin survival copula and obtain a tail dependence measure. The estimation of the parameters by maximum likelihood is discussed and the Fisher information matrix is determined. We propose an EM algorithm to estimate the parameters. Some simulations are presented to verify the performance of the direct maximum-likelihood estimation and the proposed EM algorithm. We also present a method to generate bivariate distributions from our proposed BVK distribution. Furthermore, we introduce a BVK distribution which has only an absolutely continu...
34 citations
TL;DR: The authors proposed a tractable generalization of the generalized Pareto (GP) distribution for extreme values, which is the most popular model for extreme value modeling and provides a comprehensive treatment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix.
Abstract: The generalized Pareto (GP) distribution is the most popular model for extreme values. Recently, Papastathopoulos and Tawn (Journal of Statistical Planning and Inference 143 (2013), 131-143) have proposed some generalizations of the GP distribution for improved modeling. Here, we point that Papastathopoulos and Tawn's generalizations are in fact not new and then go on to propose a tractable generalization of the GP dis- tribution. For the latter generalization, we provide a comprehensive treat- ment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix. The proposed model is shown to give a better t for the real data set used in Papastathopoulos and Tawn.
31 citations
Posted Content•
TL;DR: In this paper, the authors explore the impact of different labeling regimes on consumer attitudes towards GM products and consumer welfare, and demonstrate that voluntary labeling is superior to mandatory labeling with the higher separation cost, while mandatory labeling is not necessarily better with lower separation cost.
Abstract: Genetically modified (GM) food products and their labeling have become a major policy issue with impassioned public debates. We explore the impact of different labeling regimes on consumer attitudes towards GM products and consumer welfare. Our experimental results illustrate that these consumer attitudes do not follow the Uniform distribution as has often been assumed in the literature but instead fit an adjusted Kumaraswamy distribution. If a Uniform distribution is assumed, the advantage of mandatory labeling would be exaggerated. Using an adjusted Kumaraswamy distribution our simulation results demonstrate that voluntary labeling is superior to mandatory labeling with the higher separation cost, while mandatory labeling is not necessarily better with lower separation cost. Therefore, the governments of China and other countries with similar consumer characteristics should consider voluntary labeling for GM food while encouraging innovations that reduce the price of GM food as well as controlling the opportunistic behavior of its producers so as to enhance the advantage of voluntary labeling.
26 citations
Journal Article•
TL;DR: In this paper, the authors introduced the new Kumaraswamy-power series class of distributions, which contains some new double bounded distributions, such as the -geometric, -Poisson, -logarithmic and -binomial distributions.
Abstract: In this paper, we will introduce the new Kumaraswamy-power series class of distributions. This new class is obtained by compounding the Kumaraswamy distribution of Kumaraswamy (1980) and the family of power series distributions. The new class contains some new double bounded distributions such as the Kumaraswamy-geometric, -Poisson, -logarithmic and -binomial, which are used widely in hydrology and related areas. In addition, the corresponding hazard rate function of the new class can be increasing, decreasing, bathtub and upside-down bathtub. Some basic properties of this class of distributions such as the moment generating function, moments and order statistics are studied. Some special members of the class are also investigated in detail. The maximum likelihood method is used for estimating the unknown parameters of the members of the new class. Finally, an application of the proposed class is illustrated using a real data set.
22 citations
TL;DR: Cordeiro et al. as discussed by the authors proposed a five-parameter extended fatigue life model called the McDonald-Birnbaum-Saunders (McBS) distribution and obtained the ordinary moments, generating function, mean deviations and quantile function.
Abstract: A five-parameter extended fatigue life model called the McDonald–Birnbaum–Saunders (McBS) distribution is proposed. It extends the Birnbaum–Saunders and beta Birnbaum–Saunders [G.M. Cordeiro and A.J. Lemonte, The β-Birnbaum–Saunders distribution: An improved distribution for fatigue life modeling. Comput. Statist. Data Anal. 55 (2011), pp. 1445–1461] distributions and also the new Kumaraswamy–Birnbaum–Saunders distribution. We obtain the ordinary moments, generating function, mean deviations and quantile function. The method of maximum likelihood is used to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the McBS distribution. This model can be very useful to the analysis of real data and could give more realistic fits than other special regression models.
22 citations
TL;DR: The Kumaraswamy distribution as discussed by the authors is very similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function, which makes it much better suited than the beta distribution for computation-intensive activities like simulation modeling and the estimation of models by simulation-based methods.
Abstract: The Kumaraswamy distribution is very similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. This makes it much better suited than the Beta distribution for computation-intensive activities like simulation modeling and the estimation of models by simulation-based methods. However, in spite of the fact that the Kumaraswamy distribution was introduced in 1980, further theoretical research on the distribution was not developed until very recently (Garg, 2008; Jones, 2009; Mitnik, 2009; Nadarajah, 2008). This article contributes to this recent research and: (a) shows that Kumaraswamy variables exhibit closeness under exponentiation and under linear transformation; (b) derives an expression for the moments of the general form of the distribution; (c) specifies some of the distribution's limiting distributions; and (d) introduces an analytical expression for the mean absolute deviation around the median as a function of the parameters of the distribution, an...
22 citations
TL;DR: In this paper, the authors explore the impact of different labeling regimes on consumer attitudes towards GM products and consumer welfare, and demonstrate that voluntary labeling is superior to mandatory labeling with the higher separation cost, while mandatory labeling is not necessarily better with lower separation cost.
08 Oct 2013
TL;DR: In this article, the Kumaraswamy Generalized linear failure rate (KGLFR) was studied and some mathematical properties of the KGLFR including moments, moment generating function and quantile function were derived.
Abstract: Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy Generalized linear failure rate (KGLFR).We derive some mathematical properties of the (KGLFR) including moments, moment generating function and quantile function. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters.