Evaluation of the Laplace transform of the Pareto distribution 1.0

LAPLACEOFPARETO evaluates the Laplace-Stietljes transform (LST) of the Paretodistribution with parameters a and b. Specifically, this function evaluatesthe LST E[exp(-sX)] of a random variable $X$ which has Pareto distribution$F(x)=1-frac{b^a}{(b+x)^a}$, where s>0, a>0, b>0. The formula used canbe found in the following paper:Nadarajah, S., Kotz, S. (2006) On the Laplace Transform of the ParetoDistribution. Queueing Syst., 54, pp. 243-244. SYNOPSIS: fun=LaplaceOfPareto(s,a,b) INPUT s : argument a,b : Pareto distribution parameters (positive reals) OUTPUT fun : a vector of the same length as s; it contains NaN values for zero values of the argument s. Obtain the value of the LST at zero as a right limit, or develop this function further by using growth estimation of the incomplete gamma function at zero. REMARKS 1. This function makes use of the function gamma_incomplete: http://www.mathworks.com/matlabcentral/fileexchange/29321-evaluation-of-the-upper-incomplete-gamma-function The function gamma_incomplete.m evaluates the upper incomplete Gamma function and extends the MATLAB function gammainc. 2. The Laplace-Stieltjes transform of a probability distribution is a complete monotone function; it equals unity at s=0 iff the distribution is proper (no positive mass at infinity), and it is less than unity at s=0 if the distribution is improper; the difference 1-LST(0) is then the mass at the infinity. EXAMPLES a=2.35; b=1.98; h = 0.0001; s = h:h:100; f = LaplaceOfPareto(s,a,b); plot(s,f); a=1; b=1; h = 0.0001; s = h:h:200; f = LaplaceOfPareto(s,a,b); plot(s,f); a=0.8; b=0.1; h = 0.0001; s = h:h:500; f = LaplaceOfPareto(s,a,b); plot(s,f); a=.1; b=0.1; h = 0.0001; s = h/10:h:.1; f = LaplaceOfPareto(s,a,b); plot(s,f); a=.1; b=0.1; h = 0.0001; s = h/10:h:25; f = LaplaceOfPareto(s,a,b); plot(s,f);

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Complete,  Extends,  Gamma,  Gamma Incompletem,  Gammainc,  Laplacestieltjes,  Matlab,  Monotone,  Probability,  Upper
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