Calculate moments (mean, var, kurtosis) for the data in a gsl_vector.

Defines

#define apop_vector_mean(in)
#define apop_mean(in)
#define apop_vector_var(in)
#define apop_var(in) apop_vector_var(in)
#define apop_vector_kurt(in) apop_vector_kurtosis(in)

Functions

double apop_vector_skew (const gsl_vector *in)
double apop_vector_skew_pop (const gsl_vector *in)
double apop_vector_kurtosis_pop (const gsl_vector *in)
double apop_vector_kurtosis (const gsl_vector *in)
double apop_vector_var_m (const gsl_vector *in, const double mean)
double apop_vector_cov (const gsl_vector *ina, const gsl_vector *inb)
double apop_vector_correlation (const gsl_vector *ina, const gsl_vector *inb)

Detailed Description

These functions simply take in a GSL vector and return its mean, variance, or kurtosis; the covariance functions take two GSL vectors as inputs.

apop_vector_kurtosis and apop_vector_kurt are identical; pick the one which sounds better to you.

See also:: db_moments

For apop_vector_var_m(vector, mean), mean is the mean of the vector. This saves the trouble of re-calcuating the mean if you've already done so. E.g.,

gsl_vector *v;
double mean, var;

//Allocate v and fill it with data here.
mean = apop_vector_mean(v);
var  = apop_vector_var_m(v, mean);
printf("Your vector has mean %g and variance %g\n", mean, var);

Define Documentation

#define apop_mean ( in )

An alias for apop_vector_mean. Returns the mean of the data in the given vector.

Returns the mean of the elements of the vector v.

#define apop_var ( in ) apop_vector_var(in)

An alias for apop_vector_var. Returns the variance of the data in the given vector.

#define apop_vector_kurt ( in ) apop_vector_kurtosis(in)

Returns the sample kurtosis (divide by $n-1$ ) of the data in the given vector. This does not normalize the output: the kurtosis of a ${\cal N}(0,1)$ is three, not zero.

An alias for apop_vector_kurtosis.

#define apop_vector_mean ( in )

Returns the mean of the data in the given vector.

Returns the mean of the elements of the vector v.

#define apop_vector_var ( in )

Returns the variance of the data in the given vector.

This uses (n-1) in the denominator of the sum; i.e., it corrects for the bias introduced by using $\bar x$ instead of $\mu$ .

At the moment, there is no var_pop function. Just multiply this by (n-1)/n if you need that.

Returns the sample variance of the elements of the vector v.

Function Documentation

double apop_vector_correlation	(	const gsl_vector *	ina,
		const gsl_vector *	inb
	)

Returns the correllation coefficient of two vectors. It's just ${\hbox{cov}(a,b)\over \sqrt(\hbox{var}(a)) * \sqrt(\hbox{var}(b))}.$

double apop_vector_cov	(	const gsl_vector *	ina,
		const gsl_vector *	inb
	)

Returns the covariance of two vectors

double apop_vector_kurtosis ( const gsl_vector * in )

Returns the sample kurtosis (divide by $n-1$ ) of the data in the given vector. Corrections are made to produce an unbiased result.

This does not normalize the output: the kurtosis of a ${\cal N}(0,1)$ is three $\sigma^4$ , not three, one, or zero.

double apop_vector_kurtosis_pop ( const gsl_vector * in )

Returns the population kurtosis ( $\sum_i (x_i - \mu)^4/n)$ ) of the data in the given vector.

Some people like to normalize the skew by dividing by variance squared, or by subtracting three; those things are not done here, so you'll have to do them separately if need be.

double apop_vector_skew ( const gsl_vector * in )

Returns an unbiased estmate of the sample skew (population skew times y $n^2/(n^2-1)$ ) of the data in the given vector.

double apop_vector_skew_pop ( const gsl_vector * in )

Returns the population skew $(\sum_i (x_i - \mu)^3/n))$ of the data in the given vector.

Some people like to normalize the skew by dividing by variance $^{3/2}$ ; that's not done here, so you'll have to do so separately if need be.

double apop_vector_var_m	(	const gsl_vector *	in,
		const double	mean
	)

Returns the variance of the data in the given vector, given that you've already calculated the mean.

Parameters: