DEFINITION MODULE StatLib;
(*******************************************************************
Module StatLib (Version 0.1)
Copyright (c) 1988-2006 by Olivier Roth and ETH Zurich.
Purpose Basic statistical functions and procedures.
Remarks --
Programming
o Design
Olivier Roth 04/09/1988
o Implementation
Olivier Roth 04/09/1988
ETH Zurich
Systems Ecology
CHN E 35.1
Universitaetstrasse 16
8092 Zurich
SWITZERLAND
URLs:
<mailto:RAMSES@env.ethz.ch>
<http://www.sysecol.ethz.ch>
<http://www.sysecol.ethz.ch/SimSoftware/RAMSES>
Last revision of definition: 04/09/1988 OR
*******************************************************************)
TYPE
FunctionXProc = PROCEDURE( REAL ): REAL;
InRangeProc = PROCEDURE( REAL, REAL, REAL ): BOOLEAN;
PROCEDURE MinX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* MinX returns the minimum value of the first N reals of array X. *)
PROCEDURE MaxX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* MaxX returns the maximum value of the first N reals of array X. *)
PROCEDURE WSumX ( VAR X: ARRAY OF REAL;
N : CARDINAL;
FX : FunctionXProc ): REAL;
(* WSumX returns the weighted sum of the first N reals of array X. *)
(* Each value is weighted according to the function FX. For instance, *)
(* to compute the sum of the squares of the first 10 values of X, you *)
(* should define a function such as Square( x: REAL ): REAL; , which *)
(* returns the square of x. Once this is done, WSumX( X, 10, Square );*)
(* would return the sum of squares of the first 10 values of X. *)
PROCEDURE SumX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SumX returns the sum of X[i] for the first N values of X. *)
PROCEDURE SumXY ( VAR X, Y: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SumXY returns the sum of X[i]*Y[i] for the first N values of X and Y.*)
PROCEDURE SumX2 ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SumX2 returns the sum of X[i]^2 for the first N values of X. This *)
(* is somewhat faster than using WSumX as shown in the example above. *)
PROCEDURE SumX3 ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SumX3 returns the sum of X[i]^3 for the first N values of X. *)
PROCEDURE SumX4 ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SumX4 returns the sum of X[i]^4 for the first N values of X. *)
PROCEDURE WMeanX ( VAR X: ARRAY OF REAL;
N : CARDINAL;
FX : FunctionXProc ): REAL;
(* WMeanX returns the weighted mean of the first N reals of array X. *)
(* Each X[i] is weighted according to the function FX. *)
PROCEDURE MeanX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* MeanX returns the mean of the first N reals of array X. *)
PROCEDURE VarX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* VarX returns the variance of the first N reals of array X. *)
PROCEDURE SDevX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SDevX returns the standard deviation of the first N reals of array X.*)
PROCEDURE SkewX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* SkewX returns the skewness of the first N reals of array X.*)
PROCEDURE KurtX ( VAR X: ARRAY OF REAL; N: CARDINAL ): REAL;
(* KurtX returns the kurtosis of the first N reals of array X.*)
PROCEDURE LinearReg ( VAR X, Y : ARRAY OF REAL;
N : CARDINAL;
VAR a, b, r2 : REAL );
(* LinearReg performs linear regression analysis on the first N *)
(* values of X and Y. a and b are the coefficients of the best fit *)
(* straight line, Y= ax+b; r2 is the coefficient of determination *)
(* approaches zero as the data fail to fit a straight line. *)
PROCEDURE FuncX ( VAR X, Y: ARRAY OF REAL;
N : CARDINAL;
FX : FunctionXProc );
(* FuncX takes the first N values of array X and computes *)
(* the corresponding Y values such that Y[i]= FX( X[i] );. *)
PROCEDURE CountX ( VAR X : ARRAY OF REAL;
N : CARDINAL;
XLow, XHigh: REAL;
InRangeX : InRangeProc ): CARDINAL;
(* CountX returns the number of X values (X[0]..X[N-1]) that meet *)
(* the criteria defined by the boolean function InRangeX. See the *)
(* description of InRangeProc above. Although XLow and XHigh are *)
(* commonly used to define a continuous range, this is not necessary.*)
(* For instance, InRangeX( x, xLow, xHigh ) may be written to yield *)
(* TRUE if x is greater than XHigh or less than XLow. *)
PROCEDURE InsertX ( VAR X : ARRAY OF REAL;
N, j : CARDINAL;
xValue : REAL );
(* InsertX is an array manipulation procedure. It first shifts *)
(* X[j]..X[N-1] one index higher. xValue is then assigned to X[j]. *)
(* Notice that the overall effect is to insert xValue into X[j]. *)
(* Remember that the lower limit of open arrays is zero, and that *)
(* the value parameter N is not updated (i.e. incremented by 1). *)
PROCEDURE DeleteX ( VAR X : ARRAY OF REAL;
N, j : CARDINAL );
(* DeleteX is an array manipulation procedure. It deletes X[j] by *)
(* assigning X[i]:= X[N+1], for i:=j to N-1. This is the opposite *)
(* of InsertX. *)
PROCEDURE ClearX ( VAR X : ARRAY OF REAL;
N : CARDINAL;
xValue : REAL );
(* ClearX is an array manipulation procedure. It assigns the xValue *)
(* to the first N values of X. *)
PROCEDURE SortX ( VAR X: ARRAY OF REAL; N: CARDINAL );
(* SortX sorts the first N reals of array X in ascending order. This *)
(* is an implementation of the QuickSort algorithm. *)
PROCEDURE NormDist ( z1, z2 : REAL ): REAL;
(* NormDist returns the area under the normal distribution curve whith *)
(* a lower limit of z1 and an upper limit of z2. Note that NormDist *)
(* returns 1.0 as z1 approaches negative infinity and z2 approaches *)
(* positive infinity. If X is a random variable, then one would expect *)
(* approxiamtely 68 percent of the observed values of X to fall whithin *)
(* plus or minus one standard deviation of the mean of X. *)
PROCEDURE Factorial ( N: CARDINAL ): REAL;
(* Factorial returns N! (N factorial). *)
PROCEDURE Combination ( N, R : CARDINAL ): REAL;
(* Combination returns the number of combinations of N objects *)
(* taken R at a time. *)
PROCEDURE Permutation ( N, R : CARDINAL ): REAL;
(* Permutation returns the number of permutations of N objects *)
(* taken R at a time. *)
END StatLib.
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