The Reflected-Shifted-Truncated Lomax Distribution: Associated Inference with Applications

In health related studies, we sometimes come across left-skewed heavy-tailed survival data and vary often the probability distributions proposed in the literature to fit the model of such survival data is not adequate. In this article, we explore a new probability density function with bounded domain. The new distribution arises from the Lomax distribution proposed by Lomax (J Am Stat Assoc 49:847–852, 1954). The new transformed model, called the reflected-shifted-truncated Lomax (RSTL) distribution can be used to model left skewed data. It presents the advantage of not including any special function in its formulation. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right censored data. To assess the performance of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. The flexibility and better fitness of the new family, is demonstrated by providing well-known examples that involve complete and right censored data. Using information theoretic criteria, we compare the RSTL distribution to the Exponential, Generalized F, Generalized Gamma, Gompertz, Log-logistic, Log-normal, Rayleigh, Weibull and reflected-shifted-truncated gamma (RSTG) distributions in two negatively skewed real data sets: complete (uncensored) burial data and right censored diabetic data. Our study suggests that the RSTL distribution works better than the aforementioned nine distributions based on four different information theoretic criteria.