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Register a new userThe extended xgamma distribution
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Added by
Mahendra Saha
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al. ($2016$)]. Some important statistical properties, viz., survival characteristics, moments, mean deviation and random number generation have been derived. Further, maximum likelihood estimation for the estimation of the unknown parameters have also been discussed for the complete sample. The application of the proposed model has been illustrated through a real data set and observed that the proposed model might be taken as an better alternative to some well known lifetime distributions.
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Several representations of the exact cdf of the sum of squares of n independent gamma-distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution by Laha, an expansion of the exact distribution of the sample variance is derived by a Taylor series approach with the former distribution as its leading term. In particular for integer orders alpha some further series are provided, including a convex combination of gamma distributions for alpha = 1 and nearly of this type for alpha > 1. Furthermore, some representations of the distribution of the angle Phi between (X1,...,Xn) and (1,...,1) are given by orthogonal series. All these series are based on the same sequence of easily computed moments of cos(Phi).
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{alpha, beta}(lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that the proposed distribution function contains the standard fractional Poisson distribution as a subset. A possible interpretation of the additional parameter $beta$ is suggested.
We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distribution due to Leon and Perron (2003) and Talagrand (1994). We also establish a convex ordering for sampling without replacement from populations of real numbers between zero and one: a population of all zeros or ones (and hence yielding a hypergeometric distribution in the upper bound) gives the extreme case.
This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The proposed model is very flexible and positively skewed. Different statistical properties of the proposed model, viz., reliability characteristics, moments, generating function, mean deviation, quantile function, conditional moments, order statistics, reliability curves and indices and random variate generation etc. have been derived. The estimation of the of the survival and hazard rate functions of the EXGD has been approached by different methods estimation, viz., moment estimate (ME),maximum likelihood estimate (MLE), ordinary least square and weighted least square estimates (LSE and WLSE), Cram`er-von-Mises estimate (CME) and maximum product spacing estimate (MPSE). At last, one medical data set has been used to illustrate the applicability of the proposed model in real life scenario.
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