scholarly journals Ray calculations of ocean sound channels using a pocket programmable calculator and extended forms of the Hirsch–Carter mathematical model with tables of the Incomplete Beta Function

1979 ◽  
Vol 65 (4) ◽  
pp. 1061-1065
Author(s):  
L. Baxter
Keyword(s):  
Mathematical Model ◽  
Beta Function ◽  
Incomplete Beta Function ◽  
Programmable Calculator

Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter

2021 ◽  
Vol 127 (1) ◽  
pp. 111-130
Author(s):  
Dimitris Askitis
Keyword(s):  
Distribution Function ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Beta Function ◽  
Incomplete Beta Function ◽  
Univariate Function ◽  
Convexity Properties ◽  
Logarithmic Concavity ◽  
Two Parameter ◽  
Monotonicity Results

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

Sign in / Sign up

Export Citation Format

Share Document