HISTOGAUSS E: Histograms data and overlays it with a Gaussian. Draws the mean, sigma, and number of points on the plot. G SEQUENCE: HISTOGAUSS, Sample, A, [XX, YY, GX, GY, /NOPLOT, /NOFIT, FONT=, CHARSIZE = ] SAMPLE = Vector to be histogrammed ARGUMENTS: A = coefficients of the Gaussian fit: Height, mean, sigma A[0]= the height of the Gaussian A[1]= the mean A[2]= the standard deviation A[3]= the half-width of the 95% conf. interval of the standard mean A[4]= 1/(N-1)*total( (y-mean)/sigma)^2 ) = a measure of normality Below: superceded. The formula is not entirely reliable. A[4]= measure of the normality of the distribution. =1.0, perfectly normal. If no more than a few hundred points are input, there are formulae for the 90 and 95% confidence intervals of this quantity: M=ALOG10(N-1) ; N = number of points T90=ABS(.6376-1.1535*M+.1266*M^2) ; = 90% confidence interval IF N LT 50 THEN T95=ABS(-1.9065-2.5465*M+.5652*M^2) $ ELSE T95=ABS( 0.7824-1.1021*M+.1021*M^2) ;95% conf. (From Martinez, J. and Iglewicz, I., 1981, Biometrika, 68, 331-333.) XX = the X coordinates of the histogram bins (CENTER) YY = the Y coordinates of the histogram bins GX = the X coordinates of the Gaussian fit GY = the Y coordinates of the Gaussian fit AL INPUT KEYWORDS: /NOPLOT - If set, nothing is drawn /FITIT If set, a Gaussian is actually fitted to the distribution. By default, a Gaussian with the same mean and sigma is drawn; the height is the only free parameter. CHARSIZE Size of the characters in the annotation. Default = 0.82. FONT - scalar font graphics keyword (-1,0 or 1) for text /WINDOW - set to plot to a resizeable graphics window _EXTRA - Any value keywords to the cgPLOT command (e.g. XTITLE) may also be passed to HISTOGAUSS TINE CALLS: BIWEIGHT_MEAN, which determines the mean and std. dev. AUTOHIST, which draws the histogram GAUSSFIT() (IDL Library) which does just that ON HISTORY: Written, H. Freudenreich, STX, 12/89 More quantities returned in A, 2/94, HF Added NOPLOT keyword and print if Gaussian, 3/94 Stopped printing confidence limits on normality 3/31/94 HF Added CHARSIZE keyword, changed annotation format, 8/94 HF Simplified calculation of Gaussian height, 5/95 HF Convert to V5.0, use T_CVF instead of STUDENT_T, GAUSSFIT instead of FITAGAUSS W. Landsman April 2002 Correct call to T_CVF for calculation of A[3], 95% confidence interval P. Broos/W. Landsman July 2003 Allow FONT keyword to be passed. T. Robishaw Apr. 2006 Use Coyote Graphics for plotting W.L. Mar 2011 Better formatting of text output W.L. May 2012