Dataplot Vol 2 Vol 1

# MUTCHAZ

Name:
MUTCHAZ (LET)
Type:
Library Function
Purpose:
Compute the Muth cumulative hazard function with shape parameter .
Description:
The standard Muth distribution has the following cumulative hazard 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.

Syntax:
LET <y> = MUTCHAZ(<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 cumulative hazard 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.

Examples:
LET A = MUTCHAZ(0.3,0.2)
LET Y = MUTCHAZ(X,0.5,0,5)
PLOT MUTCHAZ(X,0.7,0,3) FOR X = 0 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 MUTCDF = Compute the Muth cumulative distribution 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.
Reference:
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.

Applications:
Distributional Modeling
Implementation Date:
2008/2
Program:
```
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 MUTCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 0.5
TITLE BETA = ^BETA
PLOT MUTCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 0.7
TITLE BETA = ^BETA
PLOT MUTCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 1
TITLE BETA = ^BETA
PLOT MUTCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Muth Cumulative Hazard Functions
```

Date created: 2/14/2008
Last updated: 2/14/2008