On Hacking's fiducial theory of inference

Fisher's theory of fiducial inference is known to lead to mathematical inconsistencies. Hacking (1965) puts forward a new basis for fiducial inference. In this paper we have presented Hacking's theory retaining his original terminology but replacing his notation by more usual mathematical notation. His condition of irrelevance is derived in an explicit mathematical form, making it more comprehensible to statisticians. Further an example is constructed to show that Hacking's theory also leads to mathematical inconsistencies.     

Exponentiated Teissier distribution with increasing,decreasing and bathtub hazard functions

This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.