Later, the moments of the ew distribution were derived by choudhury 2005. The beauty and importance of the new distribution lies in its ability to model nonmonotonic failure rate functions, which are quite common in lifetime data analysis and reliability. Aug 17, 2017 in this article, we introduced and studied exponentiated generalized kumaraswamy distribution. Description usage arguments value authors references examples. Of course, limiting distributions with respect to parameters are always interesting. Also, hamid 8 studied burr xii distribution under progressive typeii censoring. We present two reallife data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to weibull or gamma distribution and in the other data set wei. We consider three baseline distributions, namely, frechet, loglogistic, and generalized halfnormal. The cdf and pdf of the loglogistic ll distribution are for t 0. The ll and expll exponentiated loglogistic distributions are clearly the most important submodels of 6 for a b 1 and a 1, respectively. This distribution can be shown as a mixture of exponential and gamma distributions. Exponentiated chen distribution let x be a nonnegative random variable with an exponentia ted chen ec distribution with parameter s. Notes on the exponentiated half logistic distribution sciencedirect.

The pdf starts at zero, increases to its mode, and decreases thereafter. In this article, we introduced and studied exponentiated generalized kumaraswamy distribution. We refer to this new distribution as the exponentiated frechet distribution. Loglogistic distribution for survival data analysis using mcmc. Several properties of the new distribution are investigated. A new family of distributions called exponentiated kumaraswamydagum ekd distribution is proposed and studied. In this paper, we have considered the estimation problem of threeparameter exponentiated loglogistic distribution. Computes pdf, cdf, quantile and random numbers, measures of inference for 19 general families of distributions. If b 1, we obtain lehmann type ii loglogistic distribution. We propose a wider distribution called the exponentiated loglogistic geometric distribution, based on a double activation approach. In the bernoulli distribution, in the exponential family, note that the logit function i. Exponentiated half logistic generated family bycordeiro et al. Then, the density function of the threeparameter exponentiated loglogistic geometric type.

The probability density function with three different. Exponentiated generalized kumaraswamy distribution with. The exponentiated odd loglogistic family of distributions. Loglogistic distribution for survival data analysis using. Research article the exponentiated half logistic family of distributions. Subsituting from pdf 3 and cdf 4 into cdf 1, then the cdf of exponentiated weibull. As increases, while is kept the same, the pdf gets stretched out to the right and its height decreases, while maintaining its shape. Section 4 provides a characterization result on type ii exponentiated loglogistic distribution based on conditional moment of gos. In this paper, we stick to the terminology of mudholkar and srivastava 1993 as the exponentiated half logistic distribution with base distribution consider as half logistic distribution. The probability density function pdf and the cumulative distribution function cdf of ll dis. Journal of statistical distributions and applications, 1 8.

Exponentiated kumaraswamydagum distribution with applications to income and lifetime data. The beauty and importance of the new distribution lies. Similarly, we also propose the regression model based on the logarithm of the exponentiated loglogistic geometric distribution with double activation, which is an extension of the exponential logistic and logistic regression models. The loglogistic distribution also known as the fisk distribution in economics is.

This family includes several well known submodels, such as dagum d, burr iii biii, fisk or loglogistic f or llog, and new submodels, namely, kumaraswamydagum kd, kumaraswamyburr iii kbiii, kumaraswamyfisk or kumaraswamyloglogistic kf or kllog. Similarly, we also propose the regression model based on the logarithm of the exponentiated log logistic geometric distribution with double activation, which is an extension of the exponential logistic and logistic regression models. Acceptance sampling plans for percentiles based on the. As increases, while is kept the same, the pdf gets stretched out to the right and its. The log logistic distribution is commonly used to model lifetimes. The loglogistic distribution is commonly used to model lifetimes. In this article, the exponentiated discrete lindley distribution is presented and studied.

We describe different methods of parametric estimations of. The ll and expll exponentiated log logistic distributions are clearly the most important submodels of 6 for a b 1 and a 1, respectively. Exponentiated generalized transformedtransformer family. The ll distribution is among the class of survival time parametric models where the hazard rate initially increases and then decreases and at times can be humpshaped. The exponentiated loglogistic geometric distribution. In this paper, we derive maximum likelihood estimators mles, uniformly minimum variance unbiased estimators and three other estimators of the probability density function and the cumulative distribution function of the exponentiated weibull distribution and compare their. In general, all above classes can be expressed within one formulation as follows. The exponentiated exponential distribution proposed by gupta and kundu 1999, 2001 is a special case of the exponentiated weibull family. Usually, x is defined on the unit interval 0, 1 and so one would hope that models based on the distribution of y would have greater applicability. Statistical measures such as quantile, moment, moment generating function and shannon entropy for. Classes of ordinary differential equations obtained for. The iel distribution is the inverse form of the exponentiated lomax distribution. In this paper, we have considered the estimation problem of threeparameter exponentiated log logistic distribution.

The log logistic distribution can be used to model the lifetime of an object, the lifetime of a organism, or a service time. They showed that the exponentiated weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates. The exponentiated halflogistic family of distributions. Bayesian estimation of threeparameter exponentiated log. Based on the generalized loglogistic family gleaton and lynch 2006 of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd loglogistic family. The exponentiatedloglogistic geometric distribution. Classes of ordinary differential equations obtained for the. Research article the exponentiated halflogistic family of. If b 1, we obtain lehmann type ii log logistic distribution. Exponentiated inverse rayleigh distribution and an. Request pdf reliability test plans for exponentiated loglogistic distribution a generalization of the loglogistic distribution, called exponentiated loglogistic. Pdf a note on exact moments of order statistics from.

These properties resemble those of the gd and the eed. In particular, the quantile function of the standard log logistic distribution is the odds ratio function itself. A note on exact moments of order statistics from exponentiated log logistic distribution. And the corresponding probability density function pdf with shape. Exponentiated generalized g distribution in newdistns.

Subsituting from pdf 3 and cdf 4 into cdf 1, then the cdf of exponentiated weibull exponential distribution, ewe,a o, takes the following form, x. Also, hamid 8 studied burr xii distribution under progressive typeii. The exponentiated loglogistic distribution introduced by rosaiah et al 2006 is considered as a probability model for the life time of the product. Also computes the cramervon misses statistic, anderson darling statistic, kolmogorov smirnov test statistic and pvalue, maximum likelihood estimates. The use of burr xii distribution in accelerated life testing models was presented by lewis 14. Reliability test plans for exponentiated loglogistic distribution. We consider three baseline distributions, namely, frechet, loglogistic, and. This article aims to introduce a generalization of the inverse rayleigh distribution known as exponentiated inverse rayleigh distribution eird which extends a more flexible distribution for modeling life data. The cumulative distribution function cdf and probability density function pdf of the random variable x with the ehld can be given by f x 1. Gumbel distribution 14, exponentiated uniform distribution 15, beta exponentiated weibull distribution 16, exponentiated loglogistic distribution 17, exponentiated kumaraswamy distribution 18, exponentiated modified weibull extension distribution 19 and exponentiated pareto distribution 20. Exponentiated weibullexponential distribution with applications. Some statistical properties of the eird are investigated, such as mode, quantiles, moments, reliability, and hazard function. Exponentiated exponential distribution abstract twoparameterexponentiatedexponentialdistributionisarightskewedunimodal distribution.

The exponentiated gompertz generated family of distributions. The ll distribution is among the class of survival time parametric models where the hazard rate initially increases and then decreases and at. This family includes several well known submodels, such as dagum d, burr iii biii, fisk or log logistic f or llog, and new submodels, namely, kumaraswamydagum kd, kumaraswamyburr iii kbiii, kumaraswamyfisk or kumaraswamy log logistic kf or kllog, exponentiated. An exponentiated half logistic distribution to develop a. Section 4 provides a characterization result on type ii exponentiated log logistic distribution based on conditional moment of gos. If x is a beta distributed random variable, then we take y log x to have the corresponding exponentiated beta distribution. The loglogistic ll distribution is widely used in practice and it is an alternative to the lognormal distribution since it presents a failure rate function that increases, reaches a peak after some finite period, and then declines gradually. Computes the pdf, cdf, quantile and random numbers of the exponentiated generalized g distribution due to cordeiro et al.

A note on exact moments of order statistics from exponentiated loglogistic distribution. Exponentiated half logistic log logistic ehlll model. Thus, the quantile function of the basic log logistic distribution with shape parameter \ k \ is the \ k \th root of the odds ratio function. Some members of the new family such as the exponentiated generalized half logistic family was discussed. The exponentiated odd log logistic family of distributions. Pdf the kumaraswamyloglogistic distribution researchgate.

The loglogistic ll distribution branded as the fisk distribution in economics possesses a rather supple functional form. Considering censored data, we use the maximum likelihood method for estimating the parameters. Computes the pdf, cdf, quantile and random numbers of the exponentiated g distribution due to gupta et al. The following r code contains an implementation of the probability density function, cumulative distribution function, quantile function, random number generation, hazard function, and cumulative hazard function of the exponentiated weibull distribution using the commands already implemented in r for the weibull distribution. Introduction in the last few decades, there have been an increased interest among statisticians in defining new generators of univariate distributions, by adding one or more shape parameters to a baseline distribution, to provide great flexibility in modelling data in. Let rt be the probability density function pdf of the random variable t2a. We discuss maximum likelihood estimation of the model parameters. It extends the class of exponentiated distributions, odd loglogistic family gleaton and lynch 2006 and any continuous distribution by adding two shape parameters. A power p 1 captures a sharper notion of diversity than. The method of maximum likelihood is used to estimate the model parameters. We derive the analytical shapes of the corresponding probability density function and the hazard.

The complementary exponentiated burrxii poisson distribution. In probability theory and statistics, the normalexponentialgamma distribution sometimes called the neg distribution is a threeparameter family of continuous probability distributions. The kumaraswamyloglogistic distribution department of. Exponentiated loglogistic lehmann type i or dagum distribution. The expressions of order statistics are also derived.

Inferences are obtained via maximum likelihood procedure. The log logistic ll distribution is widely used in practice and it is an alternative to the log normal distribution since it presents a failure rate function that increases, reaches a peak after some finite period, and then declines gradually. The function that maps to is the logistic function, which is the inverse of the logit function as shown below. Research article the exponentiated halflogistic family of distributions.

Strongly rayleigh esr measures, which are distributions of the form s sp, where s is a set, p 0 is a parameter and is an sr measure. Here we discuss the parameter estimation by using the method of. Frequentist parameter estimation of twoparameter exponentiated. The log logistic ll distribution branded as the fisk distribution in economics possesses a rather supple functional form.

Subsituting from pdf 3 and cdf 4 into cdf 1, then the cdf of exponentiated weibull exponential distribution, ewe,a o, takes the following form, xooex a. Mcdonald loglogistic distribution with an application to. The shape of the loglogistic distribution is very similar to that of the lognormal distribution and the weibull distribution. We obtain the quantile function, ordinary moments and generating function. We propose a wider distribution called the exponentiated log logistic geometric distribution, based on a double activation approach. Consider the frechet baseline cdf for and corresponding pdf discussed in section. Exponentiated weibullexponential distribution with. The parameters are estimated using likelihood based inferential procedure. The aim of this note is to provide a comprehensive treatment of the mathematical properties of this new distribution. The random variable rv z is said to have lid with one scale parameter a 0, if the cumulative distribution function cdf and the probability density function pdf are given by.

We also present a related distribution, socalled the logexponentiated kumaraswamy distribution, which extends the generalized exponential aust. The exponentiated log logistic distribution introduced by rosaiah et al 2006 is considered as a probability model for the life time of the product. We have computed mles and bayes estimates under informative and noninformative priors along with their asymptotic confidence, bootstrap and hpd intervals. We derived mathematical properties including quantile function, moment generating function, ordinary moments, probability weighted moments, incomplete moments, and renyi entropy. The zografosbalakrishnan loglogistic distribution atlantis press. An exponentiated half logistic distribution to develop a group acceptance sampling plans with truncated time. Also of interest is that the median is 1 for every value of the shape parameter. Balakrishnang zbg distribution with probability density function pdf fx and. A new threeparameter lifetime model, called the inverted exponentiated lomax iel distribution is proposed. It is observed that the pdf of the standard ehld is a decreasing function for. The transmuted exponentiated generalizedg family of. The density function corresponding to 2 is given by where is the baseline pdf.

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