Topic
Kumaraswamy distribution
About: Kumaraswamy distribution is a research topic. Over the lifetime, 213 publications have been published within this topic receiving 3393 citations. The topic is also known as: Kumaraswamy's double bounded distribution.
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24 Jun 2021
TL;DR: In this article, the authors examined the tail conditional expectation (TCE) in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas.
Abstract: Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario.
1 citations
TL;DR: In this paper, the authors considered non-Bayesian and Bayesian estimation of Kumaraswamy parameters when the data are type II hybrid, and the maximum likelihood estimates and its asymptotic variance-covariance matrix were obtained.
Abstract: In the literature, different estimation procedures are used for inference about {\color{red} Kumaraswamy} distribution based on complete data sets. But, in many life-testing and reliability studies, a censored sample of data may be available in which failure times of some units are not reported. Unlike the common practice in the literature, this paper considers non-Bayesian and Bayesian estimation of Kumaraswamy parameters when the data are type II hybrid censored. The maximum likelihood estimates (MLE) and its asymptotic variance-covariance matrix are obtained. The asymptotic variances and covariances of the MLEs are used to construct approximate confidence intervals. In addition, by using the parametric bootstrap method, the construction of confidence intervals for the unknown parameter is discussed. Further, the Bayesian estimation of the parameters under squared error loss function is discussed. Based on type II hybrid censored data, the Bayes estimate of the parameters cannot be obtained explicitly; therefore, an approximation method, namely Tierney and Kadane's approximation, is used to compute the Bayes estimates of the parameters. Monte Carlo simulations are performed to compare the performances of the different methods, and one real data set is analyzed for illustrative purposes.
1 citations
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TL;DR: In this article, the problem of estimating the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information is considered.
Abstract: Traditional statistical approaches for estimating the parameters of the Kumaraswamy distribution have dealt with precise information. However, in real world situations, some information about an underlying experimental process might be imprecise and might be represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information. We derive the maximum likelihood estimate of the parameters by using Newton Raphson as well as EM algorithm method. The estimation procedures are discussed in details and compared via Markov Chain Monte Carlo simulations in terms of their average biases and mean squared errors.
1 citations
01 Jan 2019
TL;DR: In this paper, the authors considered the stress-strength model when both the stress and the strength variables follow the two-parameter proportional hazards family or the proportional reverse hazards family.
Abstract: The stress-strength model has been widely used for reliability design of systems. The reliability of the model is defined as the probability that the strength is larger than the stress. This chapter considers the stress-strength model when both the stress and the strength variables follow the two-parameter proportional hazards family or the proportional reverse hazards family. These two distribution families include many commonly-used distributions, such as the Weibull distribution, the Gompertz distribution, the Kumaraswamy distribution and the generalized exponential distribution, etc. Based on complete samples and record values, we derive the maximum likelihood estimation for the these stress-strength reliability. We also present the generalized confidence intervals for these stress-strength reliability. The simulation results show that the proposed generalized confidence intervals work well.
1 citations
TL;DR: This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions and Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided.
Abstract: In Bayesian analysis, the well-known beta–binomial model is largely used as a conjugate structure, and the beta prior distribution is a natural choice to model parameters defined in the (0,1) range. The Kumaraswamy distribution has been used as a natural alternative to the beta distribution and has received great attention in statistics in the past few years, mainly due to the simplicity and the great variety of forms it can assume. However, the binomial–Kumaraswamy model is not conjugate, which may limit its use in situations where conjugacy is desired. This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions. Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided. An example is used to illustrate the theory, in which the exact computation and the MCMC method are compared.
1 citations