MUTCDF

MUTCDF (LET)

Library Function

Compute the Muth cumulative distribution function with shape parameter .

The standard Muth distribution has the following cumulative distribution function:

with denoting the shape parameter.

This distribution can be generalized with location and scale parameters in the usual way using the relation

with <loc> and <scale> denoting the location and scale parameters, respectively.

LET <y> = MUTCDF(<x>,<beta>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
            <y> is a variable or a parameter (depending on what <x> is) where the computed Muth cdf value is stored;
            <beta> is a number, parameter, or variable that specifies the shape parameter;
            <loc> is a number, parameter, or variable that specifies the location parameter;
            <scale> is a positive number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <loc> and <scale> are omitted, they default to 0 and 1, respectively.

LET A = MUTCDF(0.3,0.2)
LET Y = MUTCDF(X,0.5,0,5)
PLOT MUTCDF(X,0.7,0,3) FOR X = 0 0.01 5

None

None

MUTCHAZ	= Compute the Muth cumulative hazard function.
MUTHAZ	= Compute the Muth hazard function.
MUTPDF	= Compute the Muth probability density function.
MUTPPF	= Compute the Muth percent point function.
RAYPDF	= Compute the Rayleigh probability density function.
WEIPDF	= Compute the Weibull probability density function.
LGNPDF	Compute the lognormal probability density function.
EXPPDF	= Compute the exponential probability density function.
LOGPDF	= Compute the logistic probability density function.
GAMPDF	= Compute the gamma probability density function.
EWEPDF	= Compute the exponentiated Weibull probability density function.
B10PDF	= Compute the Burr type 10 probability density function.

Leemis and McQuestion (2008), "Univariate Distribution Relationships", The American Statistician, Vol. 62, No. 1, pp. 45-53.

Muth (1977), "Reliability Models with Positive Memory Derived from the Mean Residual Life Function", in The Theory and Applications of Reliability, Eds. Tsokos and Shimi, New York: Academic Press Inc., pp. 401-435.

Distributional Modeling

2008/2

 
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET BETA  = 0.2
TITLE BETA = ^BETA
PLOT MUTCDF(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 0.5
TITLE BETA = ^BETA
PLOT MUTCDF(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 0.7
TITLE BETA = ^BETA
PLOT MUTCDF(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 1
TITLE BETA = ^BETA
PLOT MUTCDF(X,BETA) FOR X = 0.01  0.01  5
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Muth Cumulative Distribution Functions