# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Maximum-likelihood Fitting - Beta Distribution - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the shape1 and shape2 parameter of the Beta distribution fitted against any data series that is specified. The computation is performed by means of the Maximum-likelihood method. In addition the PPCC Contour Plot (Probability Plot Correlation Coefficient Contour Plot) is shown.

Note: it is often not possible to find optimal values for shape1 and shape2. The reason is that the estimation algorithm need good starting values.

Special thanks to 'Kyle' for pointing out the missing 'xbar' in line 39 of the R code!

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word Data (click to load default data) 0.224565646 0.261571480 0.253029834 0.033938060 0.353208554 0.033295045 0.002171707 0.084136132 0.077468368 0.010160325 0.079746191 0.263485597 0.460389066 0.132348066 0.529154319 0.032287005 0.472190992 0.037985170 0.019795866 0.053763887 0.086771175 0.143764004 0.202780264 0.006932185 0.124637036 0.116166293 0.037363442 0.416532177 0.612491026 0.012781084 0.163992436 0.212717925 0.092409609 0.150134816 0.047430792 0.022017328 0.350262865 0.013821921 0.578796918 0.030264300 0.090627282 0.029354226 0.182663201 0.372085552 0.235142217 0.311617946 0.030548270 0.068424450 0.043757662 0.238109173 0.465951209 0.127494709 0.010810575 0.230141979 0.426687450 0.175605499 0.005595384 0.203565169 0.236888269 0.153586896 0.027445414 0.026240968 0.299075759 0.171469487 0.016355307 0.220064442 0.137054994 0.034683689 0.085767702 0.119746590 0.223347602 0.026601623 0.063485064 0.467803972 0.012650088 0.048496183 0.047170846 0.043196485 0.095073370 0.538513979 0.045034181 0.427235474 0.289835816 0.150884924 0.176887675 0.369202741 0.178461483 0.077501113 0.281105892 0.051375864 0.357311398 0.561861189 0.028342902 0.326209843 0.303994601 0.020530542 0.278139180 0.582716856 0.071720238 0.237546024 Sample Range:(leave blank to include all observations) From: To: minimum value of shape1 parameter maximum value of shape1 parameter minimum value of shape2 parameter maximum value of shape2 parameter Chart options Width: Height:

 Source code of R module library(MASS) PPCCBeta <- function(shape1, shape2, x) { x <- sort(x) pp <- ppoints(x) cor(qbeta(pp, shape1=shape1, shape2=shape2), x) } par1 <- as.numeric(par1) par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) if (par1 < 0.1) par1 <- 0.1 if (par1 > 10) par1 <- 10 if (par2 < 0.1) par2 <- 0.1 if (par2 > 10) par2 <- 10 if (par3 < 0.1) par3 <- 0.1 if (par3 > 10) par3 <- 10 if (par4 < 0.1) par4 <- 0.1 if (par4 > 10) par4 <- 10 par1h <- par1*10 par2h <- par2*10 par3h <- par3*10 par4h <- par4*10 sortx <- sort(x) c <- array(NA,dim=c(par2h,par4h)) for (i in par1h:par2h) { for (j in par3h:par4h) { c[i,j] <- cor(qbeta(ppoints(x), shape1=i/10,shape2=j/10),sortx) } } bitmap(file="test1.png") filled.contour((par1h:par2h)/10,(par3h:par4h)/10,c[par1h:par2h,par3h:par4h],xlab="shape1",ylab="shape2",main="PPCC Contour Plot - Beta") dev.off() xbar <- mean(x) xvar <- var(x) (a <- (xbar*(1-xbar)/xvar - 1)*xbar) (b <- (1-xbar)*a/xbar) (f<-fitdistr(x, "beta",list(shape1=a,shape2=b))) xlab <- paste("Beta(shape1=",round(f\$estimate[[1]],2)) xlab <- paste(xlab,", shape2=") xlab <- paste(xlab,round(f\$estimate[[2]],2)) xlab <- paste(xlab,")") bitmap(file="test2.png") myser <- qbeta(ppoints(x), shape1=f\$estimate[[1]], shape2=f\$estimate[[2]]) qqplot(myser, x, main="QQ plot (Beta)", xlab=xlab ) grid() dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Parameter",1,TRUE) a<-table.element(a,"Estimated Value",1,TRUE) a<-table.element(a,"Standard Deviation",1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"shape1",header=TRUE) a<-table.element(a,f\$estimate[1]) a<-table.element(a,f\$sd[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"shape2",header=TRUE) a<-table.element(a,f\$estimate[2]) a<-table.element(a,f\$sd[2]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")
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 Cite this software as: Wessa P., (2009), Maximum-likelihood Beta Distribution Fitting (v1.0.4) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_fitdistrbeta.wasp/ The R code is based on : Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S., Fourth edition., Springer.
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 To cite Wessa.net in publications use:Wessa, P. (2013), Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7, URL http://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.1.23-r7Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net