  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.
