Title: What do angles of cornea curvature reveal? a new (Sinusoidal) probability density function with statistical properties assists

Authors: Ramalingam Shanmugam

Addresses: School of Health Administration, Texas State University, San Marcos, TX, 78666, USA

Abstract: This paper introduces a new probability distribution with statistical properties. It is named Sinusoidal probability distribution (SPD). The paper demonstrates an approach to analyse cornea angles' curvature as it happened among the 23 patients in a glaucoma clinic. Expressions are derived for survival and odds functions, their tipping points, its convexity, Q-Q plotting positions, variance-mean relation, heterogeneity among cornea patients, vitality function, total value at risk, past life function, entropy, hazard, inverse, and mean functions. The minimum and maximum sample values are shown to be the maximum likelihood estimators of the parameters of SPD. The joint probability density function for the lower and upper record values of a sample from SPD with their correlation function is derived and utilised to better understand the implications of the measured cornea angles. A few comments are made in the end to further advance the research in cornea illness.

Keywords: survival function; new probability density function; mean-variance relation; glaucoma incidences; cornea; curvature; odd function; Q-Q plot; heterogeneity; value at risk; entropy.

DOI: 10.1504/IJDS.2020.109498

International Journal of Data Science, 2020 Vol.5 No.1, pp.53 - 78

Received: 17 Jan 2020
Accepted: 05 May 2020
Published online: 10 Sep 2020 *

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