Half-Cauchy Gompertz Distribution : Diﬀerent Methods of Estimation

Keywords: Half-Cauchy,, Gompertz distribution,, Estimation,, MLE,, LSE and CVME.

In this paper, a new distribution called half Cauchy Gompertz distribution is

introduced. We have derived some important mathematical properties of the new

distribution like hazard function, probability density function, survival function,

cumulative distribution function, cumulative hazard function, survival function,

quantiles, the measures of skewness based on quartiles and coeﬃcient of kurtosis

based on octiles. To estimate the parameters of the new distribution we have

applied the three commonly used estimation method namely Cramer-Von-Mises

(CVM), maximum likelihood estimators (MLE), and least-square (LSE) methods.

For the assessment of potentiality of the new distribution we have consider a real

dataset and compared the goodness-of-fit attained by proposed distribution with

some competing distribution. It has been observed that the proposed model fits

the data well and more flexible as compared to some other models.