Hello,
El 16 de març de 2012 20:34, Christophe Dutang <duta...@gmail.com> ha escrit: > Hi, > > Please look at the distribution task view > (http://cran.r-project.org/web/views/Distributions.html) and the package > gamlss.dist. Thanks for the tip. There are Beta binomial functions but they don't have the number of trials parameter so I supose it's a Beta Bernoulli distribution. > > Regards > > Christophe > > -- > Christophe Dutang > Ph.D. student at ISFA, Lyon, France > website: http://dutangc.free.fr > > Le 16 mars 2012 à 18:41, Joan Maspons a écrit : > >> Hi, >> I need Beta binomial and Beta negative binomial functions ... >> >> Can I implement these new functions inside stats >> package following the >> same patterns as other probability distributions? >> >> Yours, >> -- >> Joan Maspons I have implemented a prototype of the beta negative binomial: FindParamBetaDist<- function(mu, sigma){ # return(data.frame(a=shape1,b=shape2)) # mu<- a/(a+b) [mean] # sigma<- ab/((a+b)^2 (a+b+1)) [variance] # Maxima: solve([mu= a/(a+b) , sigma= a*b/((a+b)^2 * (a+b+1))], [a,b]); a<- -(mu * sigma + mu^3 - mu^2) / sigma b<- ((mu-1) * sigma + mu^3 - 2 * mu^2 + mu) / sigma if (a <= 0 | b <= 0) return (NA) return (data.frame(a,b)) } #Rmpfr::pochMpfr()? pochhammer<- function (x, n){ return (gamma(x+n)/gamma(x)) } # PMF: # P (X = x) = ((alpha)_n (n)_x (beta)_x)/(x! (alpha+beta)_n (n+alpha+beta)_x) | for | x>=0 # (a)_b Pochhammer symbol dbetanbinom<- function(x, size, mu, sigma){ param<- FindParamBetaDist(mu, sigma) if (is.na(sum(param))) return (NA) #invalid Beta parameters if (length(which(x<0))) res<- 0 else res<- (pochhammer(param$a, size) * pochhammer(size, x) * pochhammer(param$b, x) / (factorial(x) * pochhammer(param$a + param$b, size) * pochhammer(size + param$a + param$b, x))) return (res) } curve(dbetanbinom(x, size=12, mu=0.75, sigma=.1), from=0, to=24, n=25, type="p") # CDF: # P (X<=x) = 1-(Gamma(n+floor(x)+1) beta(n+alpha, beta+floor(x)+1) # genhypergeo(1, n+floor(x)+1, beta+floor(x)+1;floor(x)+2, n+alpha+beta+floor(x)+1;1)) # /(Gamma(n) beta(alpha, beta) Gamma(floor(x)+2)) | for | x>=0 pbetanbinom<- function(q, size, mu, sigma){ require(hypergeo) param<- FindParamBetaDist(mu, sigma) if (is.na(sum(param))) return (NA) #invalid Beta parameters res<- numeric(length(q)) for (i in 1:length(q)){ if (q[i]<0) res[i]<- 0 else res[i]<- (1-(gamma(size+floor(q[i])+1) * beta(size+param$a, param$b+floor(q[i])+1) * genhypergeo(c(1, 1+size+floor(q[i]), 1+param$b+floor(q[i])), c(2+floor(q[i]),1+size+param$a+param$b+floor(q[i])), 1)) / (beta(param$a, param$b) * gamma(size) * gamma(2+floor(q[i])))) } return (res) } ## genhypergeo not converge. Increase iterations or tolerance? pbetanbinom(0:10x, size=20, mu=0.75, sigma=0.03) I have to investigate http://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html Any tip on how to solve the problem? -- Joan Maspons CREAF (Centre de Recerca Ecològica i Aplicacions Forestals) Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Catalonia Tel +34 93 581 2915 j.masp...@creaf.uab.cat http://www.creaf.uab.cat ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
