Beginning with the simplest functions, the book progresses to polynomials, exponential, trigonometric, Bessel, hypergeometric, and elliptic functions, as well as many more. This second edition of An Atlas of Functions with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families, of interest to scientists, engineers, and mathematicians who are concerned with the quantitative aspects of their field. Finally, wind speed data from six weather stations distributed in the state of Tocantins in Brazil is used to illustrate the applicability of the proposed methods. It is apparent from the results that the analytical bias-correction is more efficient than bootstrap resamples.
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On the other hand, both, the analytical and bootstrap methodologies, significantly reduce the biases and the mean squared errors. The numerical results show, for both parameters, that the maximum likelihood estimators are highly biased, especially in small samples. Secondly to derive the analytical bias-corrected maximum likelihood estimators applying the Cox and Snell methodology and thirdly to study, by Monte Carlo simulations, the small sample properties of the maximum likelihood estimators and their bias-corrected versions, obtained from the Cox and Snell formula and by parametric bootstrap technique. Firstly, to reparametrize the Chaudhry and Ahmad distribution and present some of its basic properties. The purpose of this paper is three folded. Although its probability density curve resembles the Inverse-Gaussian, Gamma, Log- normal, Weibull and other distributions, it has been neglected in the analysis of right-skewed data.
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The Chaudhry-Ahmad distribution is a two-parameter continuous probability distribution obtained as a solution to a generalized Pearson system of differential equation.