Modeling Healthcare Data with Logistic Quantile and Uniform-Based Mixture Polynomial Distributions

Continuous healthcare data often deviate from normality, which can substantially increase the risk of making invalid inferences, given that many inferential statistical procedures rely on normality assumption. To obviate this issue, we propose a new family of non-normal distributions based on a linear combination of the quantile functions of standard logistic and uniform (0, 1) distributions. This new family of non-normal distributions is studied within three different methods: L-moments, conventional moments, and percentiles. Its performance is compared among the three methods in the context of parameter estimation and data modeling. The results of Monte Carlo simulation and bootstrapping techniques indicate that the L-moment-based estimates of parameters of L-skewness and L-kurtosis are substantially less biased than their percentile-based estimates of left–right tail-weight ratio (a measure of skewness) and tail-weight factor (a measure of kurtosis), which in turn are superior to their moment-based counterparts of skewness and kurtosis, especially for small sample sizes and higher-order moments. On the other hand, the data modeling results indicate that the percentile-based fits of the proposed distributions provide slightly better approximations to real-world healthcare data than their L-moment-based counterparts, whereas both percentile- and L-moment-based methods are superior to their conventional moment-based counterparts.