Glossary of Statistical Terminology

Abstract

Autocorrelation: In a time series, x(t), with zero mean, the statistical relationship between values of a variable taken at certain times in the series and values of a variable taken at other times (a function of the time lag, 7-, between the two series) written as Rxx(7) = E[x(t)x(t + 7-)] where E is the expected value. Autocovariance is similar except that the mean of the record is not subtracted prior to the analysis. Biased estimator: An estimator k which results in the expected value E[k] of a sample having a systematic error with respect to the true expected value; i.e. E[~] -r #x. Bin interval: A specified arbitrary interval which partitions a quantity whose number of occurrences are being measured; used for constructing a histogram (frequency of occurrence distribution) of the data set. Central limit theorem: States that the distribution of sample means taken from a large population approaches a normal (Gaussian) distribution. Chi-squared distribution: The distribution function generated by the random variable -xf + xf + +... + where X~, X2, ..., Xn are n independent random variables drawn from a normal population with zero mean. The chi-squared variable ~2 has an expected value n (mean) of n and a variance of 2n. Confidence interval: An interval which has a specified probability of containing a given parameter or characteristic. Continuous random variable: A random variable which may be characterized as a continuous function. Correlation (covariance): A quantitative measure of the interdependence or association between two variables. Countable: Either finite or denumerable. Cross-correlation: The correlation between corresponding members of two or more different series of the same duration: ifx(t) -(xl, x2, ..., Xn) andy(t) = (Yl,Y2, ...,Yn) are two series, the cross-correlation is the correlation between x(t) and y(t), or between x(t) and y(t +t) for lag t such that Rxy(r) = E[x(t)y(t + r)] (see Autocorrelation). Cumulative distribution function: The integral of the probability density function, p(x), over some specified interval, @1, x2). The integral or sum ofp(x) from -~ to x gives the cumulative total of all values whose value is less than or equal to x.