A computer program for the graphical and iterative fitting of probability density functions to biological data

Estimation of the number of normal subpopulations in an heterogeneous sample and of their parameters. A recurrent method applied to neurobiology

A method is proposed to estimate the number of subpopulations which compose a heterogeneous experimental population. The method consists of reconstructing a population sample by adding computed subpopulations, postulated to be independent. The assumption is made that each subpopulation fits a normal distribution; the method may also be generalized to other distributions laws; each subpopulation can thus be entirely defined by its mean, variance and relative weight. Recurrent adjustments of number and parameters of subpopulations are carried out in order to minimize the difference between synthetized and experimental populations. This difference was measured by the quadratic distance chi2 between the two populations. Mean, variance and weight of the computed population must then be close to those of the experimental population in order to consider the results as acceptable. This method is discussed with regard to others proposed in the literature.

On the visualisation of nonstationarities in point processes

A method is described for graphically presenting interval data, such as neural interspike intervals or electrocardiographic R-R intervals, in a form that facilitates the identification of nonstationaries. The method is essentially a plot of isoprobability contours of the cumulative interval histogram, as functions of time. A sequential algorithm is used for updating the contour-line positions. This display is used in an interactive system for visually identifying nonstationarities, and for subsequently comparing selected segments of the data quantitatively using the Kolmogorov-Smirnov test.

A computer program for fitting multimodal probability density functions

A FORTRAN IV program is described, which may be run interactively with tutorial assistance or in batch and which allows a user to selectively fit any of seven probability density functions (p.d.f.'s) or a combination of the p.d.f.'s to a unimodal or multimodal histogram of empirical data. A "best-fit", uni- or multimodal p.d.f., which may be obtained by a method of nonlinear least squares or a generated p.d.f. may be displayed on a Tektronix 4010 terminal as a continuous curve against the background of a bar, square wave, symbol or point-plot histogram. The following, supportive statistical information is also displayed: (1) Kolmogorov-Smirnov probability of goodness of fit, (2) mean square error, (3) correlation coefficient, and (4) parameter estimates. The resident driver program and six overlayable segments have been implemented on a Digital Equipment Corporation LAB-11 minicomputer (PDP-11/20).