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# wweibinv

## PURPOSE

Inverse of the Weibull distribution function

## SYNOPSIS

x = wweibinv(F,a,c)

## DESCRIPTION

``` WWEIBINV Inverse of the Weibull distribution function

CALL:  x = wweibinv(F,a,c)

x = inverse cdf for the Weibull distribution evaluated at F
a, c = parameters

The Weibull distribution is defined by its cdf

F(x;a,c) = 1 -  exp(-(x/a)^c), x>=0, a,b>0

Example:
F = linspace(0,1,100);
x = wweibinv(F,10,5);
plot(F,x)```

## CROSS-REFERENCE INFORMATION

This function calls:
 comnsize Check if all input arguments are either scalar or of common size. error Display message and abort function. nan Not-a-Number.
This function is called by:
 wweibrnd Random matrices a the Weibull distribution.

## SOURCE CODE

```001 function x = wweibinv(F,a,c)
002 %WWEIBINV Inverse of the Weibull distribution function
003 %
004 % CALL:  x = wweibinv(F,a,c)
005 %
006 %        x = inverse cdf for the Weibull distribution evaluated at F
007 %     a, c = parameters
008 %
009 % The Weibull distribution is defined by its cdf
010 %
011 %  F(x;a,c) = 1 -  exp(-(x/a)^c), x>=0, a,b>0
012 %
013 % Example:
014 %   F = linspace(0,1,100);
015 %   x = wweibinv(F,10,5);
016 %   plot(F,x)
017
018 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
019 % and Life Span Models", p. 25 ff, Marcel Dekker.
020
021
022 % Tested on: Matlab 5.3
023 % History:
024 % revised pab 24.10.2000
025 % - added comnsize, nargchk
026 % rewritten ms 15.06.2000
027
028 error(nargchk(3,3,nargin))
029
030 [errorcode, F, a, c] = comnsize(F,a, c);
031 if (errorcode > 0)
032   error ('F, a and c must be of common size or scalar');
033 end
034
035 x=zeros(size(F));
036
037 ok = ((c > 0)  & (a > 0));
038
039 k = find ((F == 1) & ok);
040 if any (k),
041   tmp=inf;
042   x(k) = tmp(ones (size(k)));
043 end
044
045 k1 = find ((F > 0) & (F < 1) & ok);
046 if any (k1),
047   x(k1)=(-log(1-F(k1))).^(1./c(k1)).*a(k1);
048 end
049
050 k2 = find(F<0 | F>1 | ~ok);
051 if any(k2),
052   tmp=NaN;
053   x(k2)=tmp(ones(size(k2)));
054 end
055
056
057
058
059
060```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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