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Abstract:
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The main objective of this paper is to introduce a family of non-normal distributions by combining a quantile function of hyperbolic secant distribution and a quadratic function of uniform distribution. The method of L-moments is used for estimation of parameters of this distribution and is contrasted with the method of conventional (product) moments. A methodology is presented for fitting this family of distributions to non-normal data arising in various fields such as public health and healthcare using L-moment and conventional moment-based approaches, respectively. Also presented is a methodology for simulating correlated non-normal distributions based on the L-correlation and Pearson correlation approaches. The estimates of parameters of L-moments are substantially less biased and less dispersed compared to those based on conventional moments. Also, the estimates of L-correlation are less biased and less dispersed than those of Pearson correlation. In terms of data fitting, L-moment based fits are better than the conventional moment-based fits.
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