Degree Of Peakedness Research Articles

On application of the univariate Kotz distribution and some of its extensions

Despite a flourishing activity, especially in recent times, for the study of flexible parametric classes of distributions, little work has dealt with the case where the tail weight and degree of peakedness is regulated by two parameters instead of a single one, as it is usually the case. The present contribution starts off from the symmetric distributions introduced by Kotz in 1975, subsequently evolved into the so-called Kotz-type distribution, and builds on their univariate versions by introducing a parameter which allows for the presence of asymmetry. We study some formal properties of these distributions and examine their practical usefulness in some real-data illustrations, considering both symmetric and asymmetric variants of the distributions.

W-Peakedness: A Simulation based Study

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

A note on finding peakedness in bivariate normal distribution using Mathematica

Peakedness measures the concentration around the central value. A classical standard measure of peakedness is kurtosis which is the degree of peakedness of a probability distribution. In view of inconsistency of kurtosis in measuring of the peakedness of a distribution, Horn (1983) proposed a measure of peakedness for symmetrically unimodal distributions. The objective of this paper is two-fold. First, Horn’s method has been extended for bivariate normal distribution. Secondly, to show that computer algebra system Mathematica can be extremely useful tool for all sorts of computation related to bivariate normal distribution. Mathematica programs are also provided.

Criteria and techniques for analysing cell survival data

Cell survival was studied by analyzing the inactivation probability density function and its fundamental parameters. Mean D, variance sigma 2 and mode Dmode were evaluated and a set of equations relating these parameters to the usual parameters of the multitarget, multihit and linear-quadratic models Do and n, alpha and beta, kappa and lambda are reported. The multihit equation used was an extension of the usual equation, to allow parameter kappa to assume values that are not necessarily integers. In the multitarget curve, the mode of inactivation probability density function, proved to be the quasi-threshold dose Dq = Do ln(n). Relative variance, degree of asymmetry and degree of peakedness can be calculated from the shape parameters n in the multitarget model, kappa in the multihit model, and alpha/square root of beta in the linear-quadratic model. From an analysis of eight published cell survival sets of data, on C3H10T1/2 cells exposed to low LET radiations, it was found that D, sigma, and SF2 are the parameters which exhibit the least variation from experiment to experiment and the least variation in selecting the range of data available for estimation.

Elements of Statistical Reasoning

Elements of Statistical Reasoning E. B. Wilson CopyRight https://doi.org/10.2105/AJPH.30.7.838-a Published Online: August 29, 2011