@yahoo.ca> Subject: Re: [R] Weibull distribution Message-ID: <[EMAIL PROTECTED]> X-mailer: Foxmail 6, 3, 103, 21 [cn] Mime-Version: 1.0 Content-Type: multipart/alternative; boundary="=====003_Dragon527446281311_====="
This is a multi-part message in MIME format. --=====003_Dragon527446281311_===== Content-Type: text/plain; charset="gb2312" Content-Transfer-Encoding: 7bit Hi William, Thanks a lot for your response. I checked the package and found that what I want to solve was the opposite, that is, from mean and sd to parameters shape and scale. Could anyone give some hints please? Any suggestion would be appreciated! Leaf ----- Original Message ----- From: William Asquith, [EMAIL PROTECTED] Sent: 2006-07-17, 16:18:31 To: Leaf Sun, [EMAIL PROTECTED] Subject: Re: [R] Weibull distribution Do not have answer per se, but if you are seeking some comparisons-- try three parameter Weibull as implemented by the lmomco package. William On Jul 17, 2006, at 1:18 PM, Leaf Sun wrote: > Hi all, > > By its definition, the mean and variance of two-par. Weibull > distribution are: > > > > > > (www.wikipedia.org) > > > I was wondering, if given mean and sd. could we parameterize the > > distribution? I tried this in R. > > gamma.fun <- function(mu,sd,start=100) > { > f.fn <- function(alpha) sd^2-mu^2/(gamma(1+1/alpha))^2*(gamma(1+2/ > alpha)-(gamma(1+1/alpha))^2) > alpha <- optim(start, f.fn,method='BFGS') > beta <- mu/gamma(1+1/alpha$par) > return(list=c(a=alpha$par,b=beta)); > } > > > But the problems come up here: > > 1) the return values of a and b are only related to the input > > mean, and nothing to do with the sd. For instance, when I apply > a > mean mu = 3 whatever I use sd=2, sd=4, the function returned the > > same scale and shape values. > > > gamma.fun(3,4,10); > a b > 5.112554 3.263178 > > > gamma.fun(3,2,10); > a b > 5.112554 3.263178 > > 2) the start value determines the results: if I apply mean = 3, > and > sd=2, with a start of 10, it would return alpha close to 10, if > I > use a start = 100, it would return alpha close to 100. > > > gamma.fun(3,2,10); > a b > 5.112554 3.263178 > > > gamma.fun(3,2,100); > a b > 99.999971 3.017120 > > Since I am not a statistician, I guess there must be some > theoretical reasons wrong with this question. So I am looking > forward to some correction and advice to solve these. Thanks a > lot > in advance! > > Leaf > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting- > guide.html --=====003_Dragon527446281311_===== Content-Type: text/html; charset="gb2312" Content-Transfer-Encoding: 7bit <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=gb2312"> <META content="MSHTML 6.00.2900.2912" name=GENERATOR></HEAD> <BODY> <DIV>Hi William,</DIV> <DIV> </DIV> <DIV>Thanks a lot for your response. I checked the package and found that what I want to solve was the opposite, that is, from mean and sd to parameters shape and scale. Could anyone give some hints please? Any suggestion would be appreciated!</DIV> <DIV><BR>Leaf</DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV>----- Original Message -----</DIV> <DIV> </DIV> <DIV><FONT size=2><FONT face=Tahoma><STRONG>From:</STRONG> William Asquith, <A href="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</A><BR><B>Sent:</B> 2006-07-17, 16:18:31<BR><B>To:</B> Leaf Sun, <A href="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</A><BR><B>Subject:</B> Re: [R] Weibull distribution</FONT></FONT></DIV> <DIV> </DIV> <DIV> <TABLE width="100%"> <TBODY> <TR> <TD width="100%"> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV>Do not have answer per se, but if you are seeking some comparisons-- </DIV> <DIV>try three parameter Weibull as implemented by the lmomco package.</DIV> <DIV> </DIV> <DIV>William</DIV> <DIV>On Jul 17, 2006, at 1:18 PM, Leaf Sun wrote:</DIV> <DIV> </DIV> <DIV>> Hi all,</DIV> <DIV>></DIV> <DIV>> By its definition, the mean and variance of two-par. Weibull </DIV> <DIV>> distribution are:</DIV> <DIV>></DIV> <DIV>></DIV> <DIV>></DIV> <DIV>></DIV> <DIV>></DIV> <DIV>> (www.wikipedia.org)</DIV> <DIV>></DIV> <DIV>></DIV> <DIV>> I was wondering, if given mean and sd. could we parameterize the </DIV> <DIV>> distribution? I tried this in R.</DIV> <DIV>></DIV> <DIV>> gamma.fun <- function(mu,sd,start=100)</DIV> <DIV>> {</DIV> <DIV>> f.fn <- function(alpha) sd^2-mu^2/(gamma(1+1/alpha))^2*(gamma(1+2/ </DIV> <DIV>> alpha)-(gamma(1+1/alpha))^2)</DIV> <DIV>> alpha <- optim(start, f.fn,method='BFGS')</DIV> <DIV>> beta <- mu/gamma(1+1/alpha$par)</DIV> <DIV>> return(list=c(a=alpha$par,b=beta));</DIV> <DIV>> }</DIV> <DIV>></DIV> <DIV>></DIV> <DIV>> But the problems come up here:</DIV> <DIV>></DIV> <DIV>> 1) the return values of a and b are only related to the input </DIV> <DIV>> mean, and nothing to do with the sd. For instance, when I apply a </DIV> <DIV>> mean mu = 3 whatever I use sd=2, sd=4, the function returned the </DIV> <DIV>> same scale and shape values.</DIV> <DIV>></DIV> <DIV>> > gamma.fun(3,4,10);</DIV> <DIV>> a b</DIV> <DIV>> 5.112554 3.263178</DIV> <DIV>></DIV> <DIV>> > gamma.fun(3,2,10);</DIV> <DIV>> a b</DIV> <DIV>> 5.112554 3.263178</DIV> <DIV>></DIV> <DIV>> 2) the start value determines the results: if I apply mean = 3, and </DIV> <DIV>> sd=2, with a start of 10, it would return alpha close to 10, if I </DIV> <DIV>> use a start = 100, it would return alpha close to 100.</DIV> <DIV>></DIV> <DIV>> > gamma.fun(3,2,10);</DIV> <DIV>> a b</DIV> <DIV>> 5.112554 3.263178</DIV> <DIV>></DIV> <DIV>> > gamma.fun(3,2,100);</DIV> <DIV>> a b</DIV> <DIV>> 99.999971 3.017120</DIV> <DIV>></DIV> <DIV>> Since I am not a statistician, I guess there must be some </DIV> <DIV>> theoretical reasons wrong with this question. So I am looking </DIV> <DIV>> forward to some correction and advice to solve these. Thanks a lot </DIV> <DIV>> in advance!</DIV> <DIV>></DIV> <DIV>> Leaf</DIV> <DIV>></DIV> <DIV>> [[alternative HTML version deleted]]</DIV> <DIV>></DIV> <DIV>> ______________________________________________</DIV> <DIV>> R-help@stat.math.ethz.ch mailing list</DIV> <DIV>> https://stat.ethz.ch/mailman/listinfo/r-help</DIV> <DIV>> PLEASE do read the posting guide! <A href="http://www.R-project.org/posting-">http://www.R-project.org/posting-</A> </DIV> <DIV>> guide.html</DIV> <DIV> </DIV></BLOCKQUOTE></TD></TR></TBODY></TABLE></DIV> <DIV> </DIV> <DIV> </DIV></BODY></HTML> --=====003_Dragon527446281311_=====-- ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.