Real Statistics Release 8.8

I want to thank everyone who has made suggestions or has identified errors in the website or software. Your help has improved the utility and accuracy of Real Statistics.

I also want to express my appreciation to all of you who have donated to Real Statistics. These donations help to offset the costs of maintaining the website. If you are getting value from the Real Statistics website or software, I would appreciate your donation by going to Please Donate.

Fitting Triangular and PERT distributions

This release adds new TRIANG_FIT and PERT_FIT worksheet functions that determine the parameters of triangular and PERT distributions that best fit a data set based on the MLE approach (i.e. that maximize the log-likelihood function). See Fitting a Triangular Distribution via MLE and Fitting a PERT Distribution via MLE for details.

This release adds new TRIANG_FITM and PERT_FITM worksheet functions that determine the parameters of triangular and PERT distributions that best fit a data set based on the method of moments. See Method of Moment Support for a Triangular Distribution and Method of Moment Support for a PERT Distribution.

The new TRIANG_MLE and PERT_MLE worksheet functions have also been added that calculate the log-likelihood function value for data that follow a triangular or PERT distribution with the specified distribution parameters. See Fitting a Triangular Distribution via MLE and Fitting a PERT Distribution via MLE for details.

Holt Trend with Damping

The Holt Trend forecasting tool has been enhanced to provide an optional damping parameter. See Holt’s Linear Trend for a description of this capability without damping.

Runs Up/Down Test

The runs test (as implemented by the existing RUNSTEST function) can be used to test whether a sequence of data elements is random based on whether the number of runs of positive and negative values is random. The runs up/down test is similar, except that this test counts the number of changes in direction (increasing to decreasing value or decreasing to increasing value) as the runs count.

This release adds the following new function to implement the runs up/down test.

RunsUpDn(R1, lab, tails): returns an array with the output from the runs up/down test on the data in the column array R1.

The arguments and format of the output are as for the RUNSTEST function (see One-Sample Runs Test).

Nelder-Mead Support

The Nelder-Mead algorithm provides a way to minimize a (multivariate) function without using derivatives. This release of the Real Statistics software adds the following worksheet function:

NMEAD(R1, lab, R2, iter, prec): returns an n+2 column array whose first n values consist of the array X where f(X) is minimized (based on the Nelder-Mead algorithm), followed by the value f(X) and the number of iterations required until convergence.

Here R1 contains a lambda expression that defines the function f(X) where X is a n-dimensional random vector. See Nelder-Mead Optimization for additional details.

New Goodness-of-Fit Tests

This release adds a new worksheet function that provides a new goodness-of-fit test based on the characteristic function. The characteristic function of a probability distribution uniquely determines the characteristics of the probability distribution. The new worksheet function takes the form:

ICF_GOF(R1, dist, lab, iter, param1, param2): returns a column array with the values I-stat, I-crit for alpha = .05 and .10 for the distribution specified by dist and the data in the column array R1 (with 10 to 400 elements).

The following distributions are supported: normal, log-normal, Gumbel, Weibull, exponential, uniform, logistic, Cauchy, Laplace, and multivariate normal.

New randomized selection worksheet function

This release adds the following new worksheet function:

ExtractRandRows(R1, k): returns an array with the same number of columns as R1, but with a subset of the rows in R1. In fact, for every value in column k of R1, one row with this value is selected at random from R1 and included in the output.

Minor Enhancements

• The PERM_TEST and PERM2_TEST worksheet functions have been enhanced so that when tails = -1, the p-value of the one-tailed test with the larger p-value is returned. See Permutation Test with Paired Samples and Permutation Test for Two Independent Samples for details.
• The EVALFunc worksheet function has been added which is similar to the EVALS function. See Real Statistics Lambda Capabilities for details.
• The Ei worksheet function has been added to return the exponential integral Ei function