Discrimination between lifetime distributions with ratios of maximized likelihoods

Abstract

Major problem that often arises in the analysis of lifetime data is how to select the distribution that fits our data better among numerous models that apparently fit the data. The study investigates the procedure of ratio of the maximized likelihoods to discriminate between Weibull, Log-logistic and inverse Gaussian distributions and applies it to fit data on time-to-first-birth after marriage in Nigeria. We discriminate between two distributions at a time starting with Weibull and Log-logistic, then Weibull and inverse Gaussian and finally Log-logistic and inverse Gaussian. Ratios of maximized likelihoods computed for each of these combinations of distributions are all negative when the data set was analyzed. The study concludes by identifying inverse Gaussian distribution as the most suitable distribution to model data on time-to-first-birth in Nigeria having shown preference over Log-logistic which had initially been found to be more suitable than Weibull. The Kolmogorov-Smirnov (K-S) distance between the empirical cumulative distribution function (ecdf) and cumulative distribution function (cdf) of inverse Gaussian is 0.0873, the shortest of all the distributions investigated, points to inverse Gaussian as the most preferred distribution for the data.