;; @module stat.lsp ;; @description Basic statistics library ;; @version 1.3 - comments redone for automatic documentation ;; @author Lutz Mueller, 2001 ;; ;;

Functions for statistics and plotting with GNU plot

;; To use this module it has to be loaded at the beginning of the ;; program file: ;;

;; (load "/usr/local/share/newlisp/stat.lsp")
;;

;; All functions work on integers and floats or a mix of both. are normal ;; LISP lists. are lists of lists, one list for each row in the ;; two dimensional data matrix. See the function 'stat:matrix' on how to make matrices ;; from lists. ;; ;; This file also shows how to use some of the built in matrix math functions ;; like 'multiply', 'transpose', 'invert' and 'fft'. ;; ;; Note, that the plot functions need 'gnuplot' installed, a free graphing ;; package available for most operating systems, see: @link http://www.gnuplot.org www.gnuplot.org ;; ;; This is the oldest module written in newLISP. Some parts could be rewritten for faster ;; performance on big data sets using arrays instead of lists. ;;
;;

Plot functions (requires 'gnuplot')

;; ;; The current directory for newLISP should be writable to use these functions. ;; ;; @syntax (stat:plot ... ) ;; @param First value to plot. ;; @param Second value to plot. ;; @param Nth value to plot. ;; @return The process ID of the gnuplot process. ;; ;; @syntax (stat:plotXY X Y) ;; @param List of x-coordinates to plot. ;; @param List of y-coordinates to plot. ;; @return The process ID of the gnuplot process. ;;
;;

General uni- and bi- variate statistics

;; ;; @syntax (stat:sum ) ;; @param A list of numbers, ;; @return Sum of data in list . ;; @syntax (stat:mean ) ;; @param A list of numbers. ;; @return The mean of data in list . ;; @syntax (stat:var ) ;; @param A list of numbers. ;; @return The variance of the data in list . ;; @syntax (stat:sdev ) ;; @param A list of numbers. ;; @return Standard deviation of data in list . ;; @syntax (stat:sum-sq ) ;; @param A list of numbers. ;; @return Sum of data elements in list . ;; @syntax (stat:sum-xy ) ;; @param A list of numbers. ;; @param A list of numbers. ;; @return Sum of products data elements in lists and . ;; @syntax (stat:cov ) ;; @param A list of numbers. ;; @param A list of numbers. ;; @return Covariance of data in lists and ;; @syntax (stat:sum-d2 ) ;; @param A list of numbers. ;; @return Sum of squared diffs <(x - mean(X))^2> in list . ;; @syntax (stat:corr ) ;; @param A list of numbers. ;; @param A list of numbers. ;; @return Correlation coefficient of lists and . ;; @syntax (stat:regression ) ;; @param A list of numbers. ;; @param A list of numbers. ;; returns <(b0 b1)> coefficients of regression . ;; @syntax (stat:fit ) ;; @param A list of numbers. ;; @param A list of numbers. ;; @return fitted line based on '(stat:regression X Y)'. ;; @syntax (stat:sum-d2xy ) ;; @return Sum of squared differences <(x - y)^2> of elements in lists and . ;; @syntax (stat:moments ) ;; @param A list of numbers. ;; @return Calculates all moments of list . ;; ;; @syntax (stat:f-prob ) ;; @param The variance ratio. ;; @param Degrees of freedom. ;; @param Degrees of freedom. ;; @return Probablity of F variance ratio for , degress of freedom. ;;
;;

Multi variate statistics

;; ;; @syntax (stat:multiple-reg ) ;; @param A list of numbers. ;; @param Zero based offset into . ;; @return Multiple regression of vars in onto at . ;; @syntax (stat:cov-matrix ) ;; @param A list of numbers. ;; @return Covariance matrix of with rows and columns. ;; @syntax (stat:corr-matrix ) ;; @param A list of numbers. ;; @return Correlation matrix of with rows and columns. ;;
;;

Time series

;; ;; @syntax (stat:smooth ) ;; @param A list of numbers. ;; @param Smoothing coefficient <0 < alpha < 1>. ;; @return Exponentially smoothed sequence in . ;; @syntax (stat:lag ) ;; @param A list of numbers. ;; @param Lag n. ;; @return A differenced list of with a lag of . ;; If the length of list is then the length of the resulting ;; differenced list is . ;; @syntax (stat:cumulate ) ;; @param A list of numbers. ;; @return The cumulated list of . ;; @syntax (stat:power ) ;; @param A time series of numbers. ;; @return The power spectrum of a time series ;;
;;

Matrix and list utilities