A modified generalized exponential distribution for negatively skewed survival data

Abstract

A new distribution referred to as the reflected, shifted, truncated, generalized exponential (RSTGE) distribution is proposed to model negatively skewed data. We estimate model parameters using a hybrid method of percentile and maximum likelihood estimation. The performance of the proposed hybrid method is evaluated through Monte Carlo simulations. Estimators are evaluated using root mean squared error and average deviation. We compare the RSTGE distribution to the exponential, generalized F, generalized gamma, Gompertz, log-logistic, log-normal, Rayleigh, and Weibull distributions in negatively skewed real data sets with complete, right censored and interval censored observations. Our study suggests that the new distribution performs better than the eight distributions mentioned above when modeling complete, mildly right-censored, or interval-censored data, and is comparable with those that appropriately model heavily right-censored data.

Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 51-77.