Lehmann-type family of location-scale t distributions with two degrees of freedom

This article introduces a three-parameter Lehman-type t distribution having 2 degrees of freedom, that is capable of fitting positive and negative skewed data sets. It is shown that the density and hazard functions of the proposed distribution are uni-model. Ordinary moments, entropy measure, ordering, identifiability and order statistics are investigated. Since the quantile function is explicitly defined, quantile-based statistics are also discussed for the proposed distribution. These properties include measures of skewness and kurtosis, L-moments, quantile density and hazard functions, mean residual life function and Parzen's score function. Mechanisms of maximum likelihood, bias correction and matching of percentiles are employed for estimating the unknown parameters of the distribution. Simulation experiments are conducted to compare the performance of these three estimation methods. A real-life data set consisting of strength of glass fibres is fitted to show the adequacy of the proposed distribution over some extensions of the normal and t distributions. Parametric regression model is developed along with its parameter estimation using the maximum likelihood approach. Simulation study for the regression model is also presented that endorsed the asymptotic properties of the estimators.