By equal mean, two skew-symmetric families with the same kernel are quite similar, and the tails are often very close together. We use this observation to approximate the tail distribution of the skew-normal by the skew-normal-Laplace, and accordingly obtain a normal function approximation to...

A severe limitation of the original autoregressive process of order one or AR(1) process is the Gaussian nature of the assumed residual error distribution while the observed sample residual errors tend to be much more skewed and have a much higher kurtosis than is allowed by a normal...

A three parameter Gaussian exponential approximation to some compound Poisson distributions is considered. It is constructed by specifying the reciprocal ot the mean excess function as a linear affine function below some threshold and a positive constant above this threshold.

Based on the notions of value-at-risk and expected shortfall, we consider two functionals, abbreviated VaR and RaC, which represent the economic risk capital of a risky business over some time period required to cover losses with a high probability. These functionals are consistent with the risk...

The normal inverted gamma mixture or generalized Student t and the symmetric double Weibull, as well as their logarithmic counterparts, are proposed for modeling some loss distributions in non-life insurance and daily index return distributions in financial markets...

A number of more or less well-known, but quite complex, characterizations of stop-loss order are rewewed and proved m an elementary way. Two recent proofs of the stop-loss order preserwng property for the distortion pricing principle are invahdated through a simple counterexample...

A severe limitation of the original autoregressive process of order one or AR(1) process is the Gaussian nature of the assumed residual error distribution while the observed sample residual errors tend to be much more skewed and have a much higher kurtosis than is allowed by a normal...

A simple one-parameter analytical extension of Benford™s law for first digits of numerical data is constructed. Based on the maximum likelihood method, the fitting capabilities of the new distribution is illustrated at some interesting and important integer sequences including the numeri...

The exact probability distribution of the first digit of integer powers up to an arbitrary but fixed number of digits is derived. Based on its asymptotic distribution, it is shown that it approaches Benford's law very closely for sufficiently high powers

Given integer-valued and more general real-valued wagers, Feller(1968), Ethier and Khoshnevisan(2002) have established upper and lower bounds on the probability of ruin, which often turn out to be very close to each other. However, the exact calculation of these bounds depends on the unique...