pgfDwaring {Compounding} | R Documentation |
This function calculates value of the pgf's first derivative of the Waring distribution.
pgfDwaring(s, params)
s |
Value of the parameter of the pgf. It should be from interval [-1,1]. In the opposite pgf diverges. |
params |
List of the parameters of the Waring distribution, such that params<-c(c,a), where $c>a$ and both parameters are positive. |
S. Nadarajah, B. V. Popovic, M. M. Ristic
Johnson N, Kotz S, Kemp A (1992) Univariate Discrete Distributions, John Wiley and Sons, New York
Hankin R.K.S, Lee A (2006) A new family of non-negative distributions. Australia and New Zealand Journal of Statistics 48(1): 67(78)
http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf
params<-c(.8,.4) pgfDwaring(.5,params) ## The function is currently defined as pgfDwaring <- function(s,params) { require(hypergeo) k<-s[abs(s)>1] if (length(k)>0) warning("At least one element of the vector s are out of interval [-1,1]") if (length(params)<2) stop("At least one value in params is missing") if (length(params)>2) stop("The length of params is 2") cc<-params[1] a<-params[2] if (cc<=0) stop ("Parameter c must be positive") if (a<=0) stop ("Parameter a must be positive") a*(cc-a)/(cc*(cc+1))*Re(hypergeo(2,a+1,cc+2,s)) }