Results 21 to 30 of about 5,394,885 (148)

Necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic

, 2020
In the paper, by convolution theorem of the Laplace transforms, Bernstein's theorem for completely monotonic functions, and logarithmic concavity of a function involving exponential functions, the author(1) finds necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic on the right real semi-axis; and ...
Feng Qi (祁锋)
openaire   +3 more sources

Inequalities for Means Regarding the Trigamma Function

Journal of Nepal Mathematical Society
Let G(α, β), A(α, β) and H(α, β), respectively, be the geometric mean, arithmetic mean and harmonic mean of α and β. In this paper, we prove that G(ψ′ (z), ψ′ (1/z)) ≥ π2/6, A(ψ′ (z), ψ′ (1/z)) ≥ π2/6 and H(ψ′ (z), ψ′ (1/z)) ≤ π2/6. This extends the previous results of Alzer and Jameson regarding the digamma function ψ.
Kwara Nantomah, Gregory Abe-I-Kpeng, Sunday Sandow   +2 more
exaly   +2 more sources

Poisson Beta Regression for Count Data With an Application to Hospital Length of Stay Data [PDF]

Statistics in Medicine, Volume 44, Issue 18-19, August 2025.
ABSTRACT There has been growing awareness recently that conventional models for count data, such as the Negative Binomial model and zero inflated models, often yield poor fit and sub‐optimal performance when applied to real‐world count data problems. In response, a new, more flexible model for count data, the Poisson‐Beta model, has started to attract ...
Alan Herschtal
wiley   +2 more sources

Monotonicity Properties of q-Digamma and q-Trigamma Functions

Journal of Approximation Theory, 2015
The author proves certain new monotonicity properties and related inequalities involving Jackson's \(q\)-gamma, \(q\)-digamma and \(q\)-trigamma functions. For example, denoting by \(A(x)\) the square of digamma function, and \(B(x)\) the trigamma function, then for \(q>0\) the application \(B(x) + A(x) -\log q\cdot\sqrt{A(x)}\) is completely monotonic
Necdet Batir
exaly   +4 more sources

Necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic

, 2020
In the paper, by convolution theorem for the Laplace transforms, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.
Feng Qi (祁锋)
openaire   +3 more sources

A completely monotonic function involving the gamma and trigamma functions [PDF]

Kuwait Journal of Science, 2016
In the paper the author provides necessary and sufficient conditions on $a$ for the function\begin{equation*}\frac{1}{2}\ln(2\pi)-x+\biggl(x-\frac{1}{2}\biggr)\ln x-\ln\Gamma(x)+\frac1{12}{\psi'(x+a)}\end{equation*}and its negative to be completely ...
Feng Qi
doaj   +1 more source

Probabilistic Multiple-Integral Evaluation of Odd Dirichlet Beta and Even Zeta Functions and Proof of Digamma-Trigamma Reflections

Foundations
The aim of this work was to construct explicit expressions for the summation of Dirichlet Beta functions with odd arguments and Zeta functions with even arguments. In the established literature, this is typically done using Fourier series expansions or Bernoulli numbers and polynomials.
Antonio E. Bargellini, Daniele Ritelli, Giulia Spaletta   +2 more
openaire   +2 more sources

New Closed Form Estimators for the Beta Distribution

Mathematics, 2023
In this paper, we detail closed form estimators for beta distribution that are simpler than those proposed by Tamae, Irie and Kubokawa. The proposed estimators are shown to have smaller asymptotic variances and smaller asymptotic covariances compared to ...
Victor Mooto Nawa, Saralees Nadarajah
doaj   +1 more source

Approximation for the gamma function via the tri-gamma function

Journal of Inequalities and Applications, 2017
In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series.
Xu You, Xiaocui Li
doaj   +1 more source

Computation of the Gamma, Digamma, and Trigamma Functions [PDF]

SIAM Journal on Numerical Analysis, 1994
This paper gives an approximation for gamma function that, while different, has the same form as Lanczos one. Both approximations correct Stirling's approximation with contributions from the gamma function's poles a require \(O (-\log \varepsilon)\) time independent of \(z\) to calculate \(z!\) with \(a\) relative error \(\varepsilon\).
openaire   +1 more source