The Inverse Xgamma Distribution: Statistical Properties and Different Methods of Estimation

Properties and inference for a new class of XGamma distributions with an application

“…By using the expression of the rth moment, the first and second moments of the TXG distribution are, respectively, obtained as and Hence, by Eqs. (12) and (13), the variance of the TXG distribution is easily written as The skewness and kurtosis coefficients for the TXG distribution can be calculated from the expressions where (14) Var(X)…”

“…Although it has nice statistical properties, it is a disadvantage of XGamma that the distribution has only one parameter which plays a crucial role in determining the various behaviors of the distribution. Until today, various attempts have been made by several researchers to eliminate this disadvantage of the distribution, see [9][10][11][12][13][14]. However, the XGamma distribution needs to be improved in an aspect of the ability to a model for a wide variety of data types, especially the data with the hazard rates in different forms.…”

The New Extension of Inverse Weibull Distribution with Applications of Medicine Data

“…The transmuted-XG distribution has been studied by Biçer (2019). Yadav et al (2019) introduced inverse X-Gamma distribution using the transformation = 1 . Bantan et al (2020) introduced the half-logistic XG distribution using halflogistic family.…”

Generalized inverse xgamma distribution: A non-monotone hazard rate model

“…Lifetime of any item or product must follow a particular distribution shape. In the literature, there are many lifetime distributions are available from inverse family of distributions, viz., inverse exponential [see, keller and kamath (1982)], inverse Weibull [see, keller and kamath (1982)], inverse Rayleigh [see, Voda (1972)], inverse Lindley [see, Sharma et al (2014)], inverse xgamma [see, Yadav et al (2018)] distributions and many more. Also the generalization of inverse family of distributions are available in the literature, such as, generalized inverted exponential [see, Abouammoh et al (2009)], generalized inverse gamma [see, Mead(2013)], generalized inverse lindley [see Sharma et al (2015)], exponentiated generalized inverse Weibull [see, Elbatal et al (2014)] and many more.…”

“…They have also discussed several statistical properties of IXGD and showed the superiority of IXGD among the one parameter inverted family of distributions. If X followed IXGD with scale parameter θ, then the probability density function (PDF) and cumulative distribution function (CDF) of IXGD are given as [see, Yadav et al (2018)]…”