In this study, the incomplete gamma function, an exponential function, a mixed-log function and a polynomial function were evaluated to describe the lactation curve in Moroccan Holstein-Friesian dairy cows. Data from 1990 to 1999, comprising 77130 monthly milk yields of 6029 dairy cows in 280 dairy herds, were used. Edits were carried out by considering the lactation length (5 d and

A new computational framework for evaluation of the gamma function Γ(z) over complex plane is developed. The algorithm based on interpolation by rational functions, and generalizes classical methods Lanczos (SIAM J. Numer. Anal. B 1:86–96, (1964) Spouge Anal., 31(3):931–944, (1994) (which we show are also interpolatory). This utilizes exact poles function. By relaxing this condition allowing to...

In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.

We find several new representations of the Gamma function (and related functions such as R(z) = Γ(z)/Γ(−z), Binet’s function μ(z), and ln Γ(z)) as integrals and partial-fraction-like expansions. We also present convergent and/or better versions of Stirling’s formula, fully general reflection and shift formulas for the Gamma function, new continued fractions and new error estimates (such as unde...