Descriptive Statistics and Distribution Functions in Eviews

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1 Descriptive Statistics and Distribution Functions in Eviews Descriptive Statistics These functions compute descriptive statistics for a specified sample, excluding missing values if necessary. The default sample is the current workfile sample. If you are performing these computations on a series and placing the results into a series, you can specify a sample as the last argument of the descriptive statistic function, either as a string (in double quotes) or using the name of a sample object. For example: series z "1945m m12") or w s2) where S2 is the name of a sample object and W and X are series. Note that you may not use a sample argument if the results are assigned into a matrix, vector, or scalar object. For example, the following assignment: vector(2) a series x a(1) "1945m m12") is not valid since the target A(1) is a vector element. To perform this latter computation, you must explicitly set the global sample prior to performing the calculation performing the assignment: smpl 1945: :12 a(1) To determine the number of observations available for a given series, use function. Note that where appropriate, EViews will perform casewise exclusion of data with missing values. For will use only observations for which data on both X and Y are valid. In the following table, arguments in square brackets [ ] are optional arguments: [s]: sample expression in double quotes or name of a sample object. The optional sample argument may only be used if the result is assigned to a series. For

2 @quantile, you must provide the method option argument in order to include the optional sample argument. If the desired sample expression contains the double quote character, it may be entered using the double quote as an escape character. Thus, if you wish to use the equivalent of, smpl if name = "Smith" in function, you should enter the sample condition as: series y "if name=""smith""") The pairs of double quotes in the sample expression are treated as a single double quote. Function Name correlation the correlation between X and covariance the covariance between X and Y (division @nas(x[,s]) population covariance sample covariance the covariance between X and Y (division by ). the covariance between X and Y (division by ). inner product the inner product of X and Y. number of observations number of NAs the number of non-missing observations for X in the current sample. the number of missing observations for X in the current mean average of the values in median computes the median of the X (uses the average of middle two observations if the number of observations is minimum minimum of the values in maximum maximum of the values in X.

3 @quantile(x,q[,m,s]) quantile the q-th quantile of the series X. m is an optional string argument for specifying the quantile method: "b" (Blom), "r" (Rankit- Cleveland), "o" (Ordinary), "t" (Tukey), "v" (van der Waerden), "g" (Gumbel). The default value is rank the ranking of each observation in X. The order of ranking is set using o: "a" (ascending - default) or "d" (descending). Ties are broken according to the setting of t: "i" (ignore), "f" (first), "l" (last), "a" (average - default), @stdevs(x[,s]) standard deviation population standard deviation sample standard deviation square root of the unbiased sample variance (sum-ofsquared residuals divided by ). square root of the population variance (sum-of-squared residuals divided by ). square root of the unbiased sample variance. Note this is the same variance variance of the values in X (division population variance sample variance variance of the values in X. Note this is the same calculation sample variance of the values in X (division by skewness skewness of values in kurtosis kurtosis of values in X.

4 @sum(x[,s]) sum the sum of product the product of X (note this function could be subject to sum-ofsquares geometric mean sum of the squares of X. the geometric mean of X. Statistical Distribution Functions The following functions provide access to the density or probability functions, cumulative distribution, quantile functions, and random number generators for a number of standard statistical distributions. There are four functions associated with each distribution. The first character of each function name identifies the type of function: Function Type Cumulative distribution Density or probability Quantile (inverse CDF) Random number generator Beginning @r The remainder of the function name identifies the distribution. For example, the functions for the beta @qbeta When used with series arguments, EViews will evaluate the function for each observation in the current sample. As with other functions, NA or invalid inputs will yield NA values. For values outside of the support, the functions will return zero. Note that the CDFs are assumed to be right-continuous:. The quantile functions will return the smallest value where the CDF evaluated at the value equals or exceeds the probability of interest:, where. The inequalities are only relevant for discrete distributions. The information provided below should be sufficient to identify the meaning of the parameters for each distribution.

5 Distribution Functions Beta Binomial Chi-square Exponential Extreme Value (Type I- minimum) F- distribution Gamma @rged(r) Density/Probability Function for and for, where is function. if, and 0 otherwise, where, and. Note that the degrees of freedom parameter need not be an integer. for, and. where, and. Note that the functions allow for fractional degrees of freedom parameters and. where, and. where, and.

6 Laplace Logistic Log-normal Negative Binomial Normal (Gaussian) Poisson Pareto Student's - distribution @dunif(x,a,b), and. if if for location parameter shape parameter., and 0 otherwise,, and 0 otherwise, and for, and. Note that, yields the Cauchy distribution. for and. where, and.

7 @rweib(m,a) Additional Distribution Related Functions The following utility functions were designed to facilitate the computation of p-values for common statistical tests. While these results may be derived using the distributional functions above, they are retained for convenience and backward compatibility. Function Distribution Chi-square Returns the probability that a Chi-squared statistic with degrees of freedom F-distribution Probability that an F-statistic with numerator degrees of freedom and denominator degrees of freedom @tdist(x,v) t-distribution Probability that a t-statistic with degrees of freedom exceeds in absolute value (two-sided

Distribution Fitting (Censored Data)

Distribution Fitting (Censored Data) Summary... 1 Data Input... 2 Analysis Summary... 3 Analysis Options... 4 Goodness-of-Fit Tests... 6 Frequency Histogram... 8 Comparison of Alternative Distributions...