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DISTRIB

The DISTRIB command will compute probabilities for variables. The DISTRIB command can provide critical values for use if adequate statistical tables are unavailable.

In general, the format is:

DISTRIB vars / options

The available options are:

OPTION DESCRIPTION
accuracy= Specifies the level of accuracy required for the TYPE=DAVIES option. The default is ACCURACY=1E-6. Computational time can be reduced by specifying a lower value, for example ACCURACY=.001 (that is, 1E-3).
beg= Specifies the BEGinning observation to be used for the given DISTRIB command. If not specified the current SAMPLE range is used.
bign= Specifies the population size (N) for the Hypergeometric distribution. It must be specified along with the BIGX= and N= options.
bigx= Specifies the population number of successes (X) for the hypergeometric distribution. It must be specified along with the BIGN= and N= options.
c= Specifies a parameter value for TYPE=F, BURRII, BURRIII, BURRXII, PARETO or POWER.
cdf= Saves the Cumulative Distribution Function values in the variable specified.
critical= Saves the CRITICAL values in the variable specified when the INVERSE option is being used.
df= Specifies the Degrees of Freedom. This option is used only with TYPE=T and TYPE=CHI.
df1= Specifies the Degrees of Freedom for the numerator (DF1). This option is used only with TYPE=F.
df2= Specifies the Degrees of Freedom for the denominator (DF2). This option is used only with TYPE=F.
dfvec= Specifies a vector of N elements containing the Degrees of Freedom for the TYPE=DAVIES option.
eigenval= Specifies the vector of EIGENVALues to be used with the TYPE=IMHOF option.
end= Specifies the END observation to be used for the given DISTRIB command. If not specified the current SAMPLE range is used.
h= Specifies the Precision Parameter for the t-distribution. The default is H=1 which corresponds to the most common use of the t-distribution.
inverse Computes the inverse survival function. The data in vars must contain probabilities. The INVERSE option is useful for obtaining critical values. For example, when the TYPE=CHI option is also specified the values tabulated in chi-square tables will be obtained. The INVERSE option is available with TYPE=BETA, CAUCHY, CHI, ERLANG, EXPONENTIAL, EXTREME, F, GAMMA, GEOMETRIC, IG2, LOGISTIC, NORMAL, PARETO, POWER and T.
k= Specifies the parameter K for TYPE=BURRII, BURRIII, BURRXII.
kurtosis= Specifies the population excess KURTOSIS parameter for TYPE=EDGE. The coefficient of excess kurtosis is equal to 0 for a normal distribution.
lambda= Specifies the name of an N element lamda vector to be used with TYPE=DAVIES.
limit= Specifies the maximum number of integration terms to be used with TYPE=DAVIES. The default is 10000.
llf Computes the Log of the Likelihood Function for the data and prints it and stores it in the temporary variable $LLF. This option may not be used with TYPE=IMHOF, non-central distributions, or the INVERSE option.
mean= Specifies the population MEAN value for use with TYPE=BETA, EDGE, EXPONENTIAL, NORMAL or POISSON.
n= Specifies the sample size (N) for use with TYPE=BINOMIAL or TYPE=HYPERGEO. With TYPE=DAVIES this option specifies the number of chi-square variables.
neigen= Specifies the Number of EIGENvalues to be used with TYPE=IMHOF if the entire vector is not required.
nolist Suppresses the listing of probability densities or critical values for each observation. It would normally be used only if these numbers were saved in temporary or permanent variables for later use and the listing was not required.
noncen= Specifies a vector of non-centrality parameters with the TYPE=DAVIES option.
p= Specifies a parameter value for TYPE=BERNOULLI, BETA, BINOMIAL, ERLANG, GAMMA, GEOMETRIC, NEGBIN, PASCAL or WEIBULL. This is not needed with TYPE=BETA if MEAN= and VAR= are used.
pdf= Saves the Probability Density Function for each observation in the variable specified. It may not be used with TYPE=IMHOF.
q= Specifies a parameter value for TYPE=BETA, ERLANG, GAMMA or WEIBULL. This is not needed with TYPE=BETA if MEAN= and VAR= are used.
s= Specifies a parameter value for TYPE=IG2. For TYPE=DAVIES, the S= option specifies the value of???and the default value is zero.
skewness= Specifies the population SKEWNESS coefficient for TYPE=EDGE. The coefficient of skewness is equal to 0 for a normal distribution.
type= Specifies the TYPE of distribution. If the type is not specified SHAZAM assumes TYPE=NORMAL. The other choices, are BERNOULLI, BETA, BINOMIAL, BURRII, BURRIII, BURRXII, CAUCHY, CHI, DAVIES, EDGE, ERLANG, EXPONENTIAL, EXTREME, F, GAMMA, GEOMETRIC, HYPERGEO, IG2, IMHOF, LOGISTIC, LOGNORMAL, NEGBIN, PARETO, PASCAL, POISSON, POWER, T and WEIBULL.
v= Specifies the degrees for freedom for TYPE=IG2.
var= Specifies the population VARiance. This option is only used with TYPE=NORMAL, TYPE=EDGE or TYPE=BETA.
x= Specifies a parameter value for TYPE=NEGBIN or PASCAL.

The types of distribution available on the TYPE= option are:

TYPE OF DISTRIBUTION PARAMETERS
BERNOULLI Bernoulli Distribution, parameter P=.
BETA Beta Distribution P= and Q=, or MEAN= and VAR= must be used. The beta variable must be in the 0-1 interval.
BINOMIAL Binomial Distribution, parameters N= and P=.
BURRII, BURRIII, BURRXII The Burr Distribution.
CAUCHY Cauchy Distribution (same as t with DF=1).
CHI Chi Squared Distribution DF= must be used.
DAVIES Davies Distribution.
EDGE Edgeworth Approximation MEAN=, VAR=, SKEWNESS= and KURTOSIS= should be used.
ERLANG Erlang Distribution, parameters are P= and Q=. Same as gamma with q an integer.
EXPONENTIAL Exponential distribution, parameter MEAN=.
EXTREME Extreme Value Distribution
F F Distribution
DF1= and DF2= must be used.
C= must be used for a Non-Central F Distribution.
GAMMA Gamma Distribution, parameters are P= and Q=.
GEOMETRIC Geometric Distribution, parameter P=.
HYPERGEO Hypergeometric Distribution, parameters are BIGN=, N= and BIGX=.
LOGISTIC Logistic distribution.
LOGNORMAL Lognormal distribution.
IG2 Inverted Gamma, parameters are S= and V=.
IMHOF Imhof Distribution. EIGENVAL= must be used.
NEGBIN Negative binomial distribution, parameters are P= and X=.
NORMAL Normal Distribution. MEAN=, and VAR= should be used with it.
PARETO Pareto distribution, parameter C= (default is C=1).
PASCAL Pascal distribution, parameters are P= and X=.
POISSON Poisson distribution, parameter MEAN=.
POWER Power function distribution, parameter C= (default is C=1).
T Student's t Distribution. DF= must be used.
WEIBULL Weibull distribution, parameters P= and Q=.