ProbCalculator Help Index

PROBCALC is a probability calculator.  It computes values of the distribution function, P(X <= x), the complementary distribution function, P(X >= x), values that have a specified value for the distribution function, P(X <= ?) = x, and values that have a specified value for the complementary distribution function, P(X >= ?) = x.  It does these for the binomial, chi-squared, F, standard normal, Poisson and t distributions.  The computations are made using algorithms described in Numerical Recipes in C, by William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Cambridge University Press.

Distributions

PROBCALC computes values for five distributions.  The distribution selected in the DISTRIBUTION box.  Click on the button on the right hand side of the box and then click on the desired distribution.  You then proceed as follows.

•	Binomial Distribution—The binomial distribution has two parameters—n, the number of trials, and p, the probability of success.  Selecting the binomial distribution opens the parameter dialogue box.  Enter n, which must be a positive integer, and p, which must be a value between 0 and 1 in the indicated boxes and then click OK to return to the main calculator dialogue box.

•	Chi-squared Distribution—The chi-squared distribution has one parameter—d.f., the number of degrees of freedom.  Selecting the chi-squared distribution opens the parameter dialogue box.  Enter d.f., which must be a positive integer, in the D.F. box and click OK to return to the main calculator dialogue box.

•	F Distribution—The F distribution has two parameters—degrees of freedom for the numerator and degrees of freedom for the denominator.  Selecting the F distribution opens the parameter dialogue box.  Enter the numerator degrees of freedom, which must be a positive integer, in the NUMERATOR dialogue box, the denominator degrees of freedom, which must be a positive integer, in the DENOMINATOR dialogue box, and click OK to return to the main calculator dialogue box.

•	Normal Distribution—The calculator calculates values for the standard normal distribution only.  Select the normal distribution and proceed to make your calculation.

•	Poisson Distribution—The Poisson distribution has one parameter—lambda, the mean number of events in a fixed interval.  Selecting the Poisson distribution opens the parameter dialogue box.  Enter lambda, which must be a positive number, in the LAMBDA dialogue box and click OK to return to the main calculator dialogue box.

•	T Distribution—The t distribution has one parameter—d.f., the number of degrees of freedom.  Selecting the t distribution opens the parameter dialogue box.  Enter d.f., which must be a positive integer, in the D.F. dialogue box and click OK to return to the main calculator dialogue box.

Operations

PROBCALC performs four calculations with the distribution selected.  The desired operation is selected by clicking the appropriate radio button.  You then enter the desired value for x, in the X dialogue box and click CALCULATE to perform the operation.  The value resulting from the calculation will appear in the RESULT dialogue box.

•	Distribution Function, P(X <= x)—The distribution function operation computes the probability that the selected random variable will have a value less than or equal to the value entered in the X dialogue box.

•	P(X >= x)—This operation computes the probability that the selected random variable  will have a value greater than or equal to the value entered in the X dialogue box.

•	P(X <= ?) = x—This operation computes the value of the selected random variable that has a probability of being less than or equal to it that is equal to the value entered in the X dialogue box.  It is the lower tail percentage point for that distribution.  The value entered in the X dialogue box must be between 0 and 1.  In the case of the discrete binomial and Poisson distributions, the operation returns values that bracket the value entered in the X dialogue box and the probability associated with each one.

•	P(X >= ?) = x—This operation computes the value of the selected random variable that has a probability of being greater than or equal to it that is equal to the value entered in the X dialogue box.  It is the upper tail percentage point for that distribution.  The value entered in the X dialogue box must be between 0 and 1.  In the case of the discrete binomial and Poisson distributions, the operation returns values that bracket the value entered in the X dialogue box and the probability associated with each one