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# wweibstat

## PURPOSE Mean and variance for the Weibull distribution.

## SYNOPSIS [m,v]= wweibstat(a,c);

## DESCRIPTION WWEIBSTAT Mean and variance for the Weibull  distribution.

CALL:  [m,v] = wweibstat(a,c)

m, v = the mean and variance, respectively
a, c = parameters of the Weibull distribution (see wweibcdf).

Mean (m) and variance (v) for the Weibull distribution is

m=a*gamma(1+1/c)  and  v=a^2*gamma(1+2/c)-m^2;

Example:
[m,v] = wweibstat(4,0.5)

See also  wweibcdf

## 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. gamma Gamma function. nan Not-a-Number.
This function is called by:
 dist2dcdf Joint 2D CDF computed as int F(X1 dist2dstat Mean and variance for the DIST2D distribution mdist2dstat Mean and variance for the MDIST2D distribution. weib2dcdf Joint 2D Weibull cumulative distribution function weib2dstat Mean and variance for the 2D Weibull distribution

## SOURCE CODE 001 function [m,v]= wweibstat(a,c);
002 %WWEIBSTAT Mean and variance for the Weibull  distribution.
003 %
004 % CALL:  [m,v] = wweibstat(a,c)
005 %
006 %   m, v = the mean and variance, respectively
007 %   a, c = parameters of the Weibull distribution (see wweibcdf).
008 %
009 %  Mean (m) and variance (v) for the Weibull distribution is
010 %
011 %  m=a*gamma(1+1/c)  and  v=a^2*gamma(1+2/c)-m^2;
012 %
013 % Example:
014 %   [m,v] = wweibstat(4,0.5)
015 %
017
018
019 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
020 % and Life Span Models", p. 25 ff, Marcel Dekker.
021
022
023 % Tested on; Matlab 5.3
024 % History:
025 % revised pab 23.10.2000
026 %   - added comnsize
027 % added ms 15.06.2000
028
029 error(nargchk(2,2,nargin))
030
031 [errorcode, a, c] = comnsize(a,c);
032
033 if errorcode > 0
034     error('a and c must be of common size or scalar.');
035 end
036
037 %   Initialize Mean and Variance to zero.
038 m = zeros(size(a));
039 v = zeros(size(a));
040
041 ok = (a > 0 & c > 0);
042 k = find(ok);
043 if any(k)
044   m(k) =  a(k) .* gamma(1 + (1 ./ c(k)));
045   v(k) = a(k) .^ 2 .* gamma(1 + (2 ./ c(k))) - m(k).^ 2;
046 end
047
048 k1 = find(~ok);
049 if any(k1)
050     tmp = NaN;
051     m(k1) = tmp(ones(size(k1)));
052     v(k1) = m(k1);
053 end
054

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

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