This chapter lists and describes many of Mathcad’s built-in statistical functions. These functions perform a wide variety of computational tasks, including statistical analysis, interpolation, regression, and smoothing.

The following sections make up this chapter:

Population and sample statistics
Functions for computing the mean, variance, standard deviation, and correlation of data.

Probability distributions
Functions for evaluating probability densities, cumulative probability distributions and their inverses for over a dozen common distribution functions.

Histogram function
now to count the number of data values falling into specified intervals.

Random numbers
Generating random numbers having various distributions.

Interpolation and prediction functions
Linear and cubic spline interpolation. Functions for multivariate interpolation.

Regression functions
Functions for linear regression, polynomial regression, and regression using combinations of arbitrary functions.

Smoothing functions
Functions for smoothing time series with either a running median, a Gaussian kernel, or an adaptive linear least-squares method.

Population and sample statistics

Mathcad includes eight functions for population and sample statistics. In the following descriptions, m and n represent the number of rows and columns in the pecified arrays. In the formulas below, the built-in variable ORIGIN is set to its default value of zero.

Probability distributions

Mathcad includes several functions for working with several common probability densities. These functions fall into three classes:

Probability densities: These give the likelihood that a random variable will take on a particular value.

Cumulative probability distributions: These give the probability that a random variable will take on a value less than or equal to a specified value. These are obtained by simply integrating (or summing when appropriate) the corresponding probability density over an appropriate range.

Inverse cumulative probability distributions: These functions take a probability as an argument and return a value such that the probability that a random variable will be less than or equal to that value is whatever probability you supplied as an argument.

Probability densities

These functions return the likelihood that a random variable will take on a particular value. The probability density functions are the derivatives of the corresponding cumulative distribution functions discussed in the next section.

Returns the probability density for the beta distribution:

Probability densities

Return P(X = k) when the random variable X has the binomial

Cumulative probability distributions

These functions return the probability that a random variable is less than or equal to a specified value. The cumulative probability distribution is simply the probability density function integrated from -00 to the specified value. For integer random variables, the integral is replaced by a summation over the appropriate range.

The probability density functions corresponding to each of the following cumulative distributions are given in the section “Probability distributions” on page 281. Figure 14-1 at the end of this section illustrates the relationship between these three .A functions.

Cumulative probability distributions

Cumulative probability distributions

Inverse cumulative probability distributions

These functions take a probability p as an argument and return the value of x such that P(X::;x) = p.

The probability density functions corresponding to each of the following inverse cumulative distributions are given in the section “Probability distributions;’ on page 281.

Relationship between probability densities, cumulative distributions and their inverses .

Posted on November 21, 2015 in Statistical Functions