|GNU Scientific Library Reference Manual - Third Edition (v1.12)|
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
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21.10 The histogram probability distribution struct
The probability distribution function for a histogram consists of a set of bins which measure the probability of an event falling into a given range of a continuous variable x. A probability distribution function is defined by the following struct, which actually stores the cumulative probability distribution function. This is the natural quantity for generating samples via the inverse transform method, because there is a one-to-one mapping between the cumulative probability distribution and the range [0,1]. It can be shown that by taking a uniform random number in this range and finding its corresponding coordinate in the cumulative probability distribution we obtain samples with the desired probability distribution.
- Data Type: gsl_histogram_pdf
- This is the number of bins used to approximate the probability distribution function.
double * range
- The ranges of the bins are stored in an array of n+1 elements pointed to by range.
double * sum
- The cumulative probability for the bins is stored in an array of n elements pointed to by sum.
The following functions allow you to create a
struct which represents this probability distribution and generate
random samples from it.
- Function: gsl_histogram_pdf * gsl_histogram_pdf_alloc (size_t n)
- This function allocates memory for a probability distribution with
n bins and returns a pointer to a newly initialized
gsl_histogram_pdfstruct. If insufficient memory is available a null pointer is returned and the error handler is invoked with an error code of
- Function: int gsl_histogram_pdf_init (gsl_histogram_pdf * p, const gsl_histogram * h)
- This function initializes the probability distribution p with
the contents of the histogram h. If any of the bins of h are
negative then the error handler is invoked with an error code of
GSL_EDOMbecause a probability distribution cannot contain negative values.
- Function: void gsl_histogram_pdf_free (gsl_histogram_pdf * p)
- This function frees the probability distribution function p and all of the memory associated with it.
- Function: double gsl_histogram_pdf_sample (const gsl_histogram_pdf * p, double r)
- This function uses r, a uniform random number between zero and
one, to compute a single random sample from the probability distribution
p. The algorithm used to compute the sample s is given by
the following formula,
s = range[i] + delta * (range[i+1] - range[i])
where i is the index which satisfies sum[i] <= r < sum[i+1] and delta is (r - sum[i])/(sum[i+1] - sum[i]).
|ISBN 0954612078||GNU Scientific Library Reference Manual - Third Edition (v1.12)||See the print edition|