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In this communication, we introduce a new statistical model and study itsvarious mathematical properties. The expressions for hazard rate, reversedhazard rate, and odd functions are provided. We explore the asymptoticbehaviors of the density and hazard functions of the newly proposed model.Further, moments, median, quantile, and mode are obtained. The cumulativedistribution and density functions of the general $k$th order statistic areprovided. Sufficient conditions, under which the likelihood ratio order betweentwo inverse generalized linear failure rate (IGLFR) distributed randomvariables holds, are derived. In addition to these results, we introduceseveral estimates for the parameters of IGLFR distribution. The maximumlikelihood and maximum product spacings estimates are proposed. Bayes estimatesare calculated with respect to the squared error loss function. Further,asymptotic confidence and Bayesian credible intervals are obtained. To observethe performance of the proposed estimates, we carry out a Monte Carlosimulation using $R$ software. Finally, two real-life data sets are consideredfor the purpose of illustration.

A novel distribution with upside down bathtub shape hazard rate: properties, estimation and applications