RE: Triangular Probability Distributions

*To*: mathgroup at smc.vnet.net*Subject*: [mg30020] RE: [mg30009] Triangular Probability Distributions*From*: "tgarza01 at prodigy.net.mx" <tgarza01 at prodigy.net.mx>*Date*: Sat, 21 Jul 2001 16:16:45 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello Michael, I'm not clear as to what you mean by "methodology". Still, what you may do is define the triangular probability density function and work from it. For example, if you want your density defined in the interval [a, b], In[1]:= Clear[triPdf,triCdf] In[2]:= triPdf[x_,a_,b_]:=((1+a)/(b^2-a^2))*4*(x-a)/;a<=x<=(b+a)/2; triPdf[x_,a_,b_]:=((1+a)/(b^2-a^2))*4*(b-x)/;(b+a)/2<x<=b; triPdf[x_,a_,b_]:=0/;a>x||x<b; In[3]:= Plot[triPdf[x,0,1],{x,0,1}]; Here you obtained the graph of the triangular density in [0,1]. The distribution function is then defined as In[4]:= triCdf[x_,a_,b_]:=Integrate[triPdf[y,a,b],{y,a,x}] which you plot with (it takes a little while, due to the fact that the numerical integration is slow because of the peak at x = 0.5; you may integrate one part after the other and then it runs very quickly): In[5]:= Off[NIntegrate::"ncvb"];Off[NIntegrate::"slwcon"]; In[6]:= Plot[triCdf[x,0,1],{x,0,1}]; I turned off the messages to avoid looking at them. The k-th moment is Integrate[x^k*triPdf[x,a,b],{x,a,b}] for any k. Tomas Garza Original Message: ----------------- From: loopm at yahoo.com (Michael Loop) To: mathgroup at smc.vnet.net Subject: [mg30020] [mg30009] Triangular Probability Distributions I have been looking for a methodology for using the triangular probability distribution in Mathematica. I have not found anything that allows me to do this. Has anyone found a way to use the triangular distribution? Are there any add-on packages that would include this distribution? Thank you, Michael Loop Minneapolis MN -------------------------------------------------------------------- Mail2Web - Check your email from the web at http://www.mail2web.com/ .