IMSL_SIMPLESTAT

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Version History

The IMSL_SIMPLESTAT function computes basic univariate statistics.

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Result = IMSL_SIMPLESTAT(x)

Return Value

A two-dimensional matrix containing some simple statistics for each variable x. If Median and Median_And_Scale are not used as keywords, then element (i, j) of the returned matrix contains the i-th statistic of the j-th variable. Refer to Table 13-1 for a list of results.

Arguments

x

Data matrix. The data value for the i-th observation of the j-th variable should be in the matrix element (i, j).

Keywords

CONF_MEANS

Scalar specifying the confidence level for a two-sided interval estimate of the means (assuming normality) in percent. The CONF_MEANS keyword must be between 0.0 and 100.0 and is often 90.0, 95.0, or 99.0. For a one-sided confidence interval with confidence level c, set CONF_MEANS = 100.0 – 2.0(100.0 – c) (at least 50 percent). Default: 95-percent confidence interval is computed

CONF_VARIANCES

Confidence level for a two-sided interval estimate of the variances (assuming normality) in percent. The confidence intervals are symmetric in probability (rather than in length). For one-sided confidence interval with confidence level c, set CONF_MEANS = 100.0 – 2.0(100.0 – c) (at least 50 percent). Default: 95-percent confidence interval is computed.

DOUBLE

If present and nonzero, double precision is used.

ELEMENTWISE

If present and nonzero, all nonmissing data for any variable is used in computing the statistics for that variable. Default action: if an observation (row of x) contains a missing value, the observation is excluded from computations for all variables. In either case, if weights and/or frequencies are specified and the value of the weight and/or frequency is missing, the observation is excluded from computations for all variables.

FREQUENCIES

One-dimensional array containing the frequency for each observation. Default: each observation has a frequency of 1

MEDIAN_ONLY

If present and nonzero, medians are computed and stored in elements (14, *) of the returned matrix of simple statistics. The MEDIAN_ONLY and MEDIAN_AND_SCALE keywords cannot be used together.

MEDIAN_AND_SCALE

If present and nonzero, specified, the medians, the medians of the absolute deviations from the medians, and a simple robust estimate of scale are computed and stored in elements (14, *), (15, *), and (16, *) of the returned matrix of simple statistics. The MEDIAN_ONLY and MEDIAN_AND_SCALE keywords cannot be used together.

WEIGHTS

One-dimensional array containing the weight for each observation. Default: each observation has a weight of 1.

Discussion

The IMSL_SIMPLESTAT function computes the sample mean, variance, minimum, maximum, and other basic statistics for the data in x. It also computes confidence intervals for the mean and variance (under the hypothesis that the sample is from a normal population).

Frequencies, f_i's, are interpreted as multiple occurrences of the other values in the observations. In other words, a row of x with a frequency variable having a value of 2 has the same effect as two rows with frequencies of 1. The total of the frequencies is used in computing all the statistics based on moments (mean, variance, skewness, and kurtosis). Weights, w_i's, are not viewed as replication factors. The sum of the weights is used only in computing the mean (the weighted mean is used in computing the central moments). Both weights and frequencies can be zero, but neither can be negative. In general, a zero frequency means that the row is to be eliminated from the analysis; no further processing or error checking is done on the row. A weight of zero results in the row being counted, and updates are made of the statistics.

The definitions of some of the statistics are given below in terms of a single variable x of which the i-th datum is x_i.

Mean

Variance

Skewness

Excess or Kurtosis

Minimum

x_min = min(x_i)

Maximum

x_max = max(x_i)

Range

x_max – x_min

Coefficient of Variation

Median

Median Absolute Deviation

Simple Robust Estimate of Scale

where

is the inverse of the standard normal distribution function evaluated at 3/4. This standardizes MAD in order to make the scale estimate consistent at the normal distribution for estimating the standard deviation (Huber 1981, pp. 107–108).

Example

This example uses data from Draper and Smith (1981). There are five variables and 13 observations.

x = IMSL_STATDATA(5) 
stats = IMSL_SIMPLESTAT(x) 
; Call IMSL_SIMPLESTAT. 
labels = ['means', 'variances', 'std. dev', $ 
   'skewness', 'kurtosis', 'minima', $ 
   'maxima', 'ranges', 'C.V.', 'counts', $ 
   'lower mean', 'upper mean', 'lower var', 'upper var'] 
; Define the character strings that will be used as labels for the 
; rows of the output. 
FOR i = 0, 13 DO PM, labels(i), stats(i, *), $ 
   FORMAT = '(a10, 5f9.3)' 
; Output the results. 
means        7.462     48.154     11.769     30.000     95.423 
variances   34.603    242.141     41.026    280.167    226.314 
std. dev     5.882     15.561      6.405     16.738     15.044 
skewness     0.688     -0.047      0.611      0.330     -0.195 
kurtosis     0.075     -1.323     -1.079     -1.014     -1.342 
minima       1.000     26.000      4.000      6.000     72.500 
maxima      21.000     71.000     23.000      60.000    115.900 
ranges      20.000     45.000     19.000     54.000      43.400 
C.V.         0.788      0.323      0.544      0.558      0.158 
counts      13.000     13.000     13.000     13.000      13.000 
lower mean   3.907     38.750      7.899     19.885      86.332 
upper mean  11.016     57.557     15.640     40.115     104.514 
lower var   17.793    124.512     21.096     144.065    116.373 
upper var   94.289    659.817     111.792    763.434    616.688 

Version History