We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo...

The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In this article, we define extended matrix...

In this paper we consider properties and power expressions of the functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$f:(-1,1)\rightarrow \mathbb{R }$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$f_L:(-1,1)\rightarrow \mathbb{R }$$</EquationSource> </InlineEquation>, defined by <Equation ID="Equa1"> <EquationSource Format="TEX">$$\begin{aligned} f(x;\gamma )=\frac{1}{\pi }\int \limits _{-1}^1 \frac{(1+xt)^\gamma }{\sqrt{1-t^2}}\,\mathrm{d}t \quad...</equationsource></equation></equationsource></inlineequation></equationsource></inlineequation>

<Para ID="Par1">One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on an exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace...</para>

It is proved that the average length of standard confidence intervals for parameters of Gamma and normal distributions monotonically decreases with the sample size. The proofs are based on fine properties of the classical Gamma function.

In this paper, we show a mathematical construction of Beck–Cohen superstatistics in the Bayesian point of view with the help of the two representations of a gamma function. Furthermore, it is shown how some results for superstatistics are related to each other.

An empirical model of debris-flow risk assessment is developed to estimate annual loss ratio on high-frequency debris-flow fans where more than one hazard events occur every year. Based on observations of debris flows in Jiangjia Ravine, Yunnan Province, China, it is found that Gamma...