Modified Distribution Function Research Articles

On the Calculation of the Generalised Poisson Function

Drs. H. Bohman and F. Esscher have reported in a recent paper) an extensive research performed in Sweden on the different methods of calculation of the distribution function of the total amount of claims. In the present paper certain methods are discussed in so far as they are different from those presented in the above quoted paper. The consideration is restricted to the generalised Poisson function even though some results can be easily extended. The author has already commented on some of the results represented in the sequel at a special meeting of the 17th International Congress of Actuaries in Edinburgh.I. Lemma. Let be the generalised Poisson function under investigation. If aiSi(x), where Σ ai = 1 (the functions Si need not be distribution functions, neither must the constants ai be real numbers of interval [0,1]), thenF(x; n, S) = F(.; a1n, S1) * …*F(.; arn, Sr) (x),as is easily verified by the use of characteristic functions. This component representation is repeatedly used in the sequel.2. A Modified Esscher Method. The Esscher method is based on an observation that the well-known Edgeworth expansion is more advantageously applicable to a conveniently modified distribution function instead of the original generalised Poisson function. Let us assume that the value of F(x) is required at a point

Effect of a Temperature Gradient on Thermionic Emission

The effect of a temperature gradient at the surface of a metal on the thermionic emission current is calculated. The calculation is motivated by current research in which metal surfaces are exposed to high-intensity optical maser beams with a consequent heating of the surface. A Sommerfeld free-electron model of a metal is used in which the temperature of the metal is allowed to be a function of position. A modified distribution function for the electrons is calculated using the Boltzmann transport equation from which the thermionic current is obtained. Approximations are made that limit the theory to small changes in the distribution function but the results are valid for realizable experimental conditions. It is shown in an example that for Q-switched laser intensities observable effects can be expected.