Maxima – 244 – distrib – 5

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.758.

pdf_f (x, m, n)
Returns the value at x of the density function of a F random variable F (m, n), with m, n > 0.

cdf_f (x, m, n)
Returns the value at x of the distribution function of a F random variable F (m, n), with m, n > 0.

(%i1) load ("distrib")$

(%i2) cdf_f(2,3,9/4);
                                                   9  3  3
(%o2)              1 - beta_incomplete_regularized(-, -, --)
                                                   8  2  11
(%i3) float(%);
(%o3)                         0.6675672817900802

quantile_f (q, m, n)
Returns the q-quantile of a F random variable F (m, n), with m, n > 0; in other words, this is the inverse of cdf_f. Argument q must be an element of [0, 1].

(%i4) quantile_f(2/5,sqrt(3),5);
(%o4)                         0.5189478385736898

mean_f (m, n)
Returns the mean of a F random variable F (m, n), with m > 0, n > 2.

var_f (m, n)
Returns the variance of a F random variable F (m, n), with m > 0, n > 4.

std_f (m, n)
Returns the standard deviation of a F random variable F (m, n), with m > 0, n > 4.

skewness_f (m, n)
Returns the skewness coefficient of a F random variable F (m, n), with m > 0, n > 6.

kurtosis_f (m, n)
Returns the kurtosis coefficient of a F random variable F (m, n), with m > 0, n > 8.

random_f (m, n)
random_f (m, n, k)
Returns a F random variate F (m, n), with m, n > 0. Calling random_f with a third argument k, a random sample of size k will be simulated.

The simulation algorithm is based on the fact that if X is a Chi² (m) random variable and Y is a Chi2 (n) random variable, then

is a F random variable with m and n degrees of freedom F (m, n).

pdf_exp (x, m)
Returns the value at x of the density function of an Exponential(m) random variable, with m > 0.

The Exponential(m) random variable is equivalent to the Weibull(1, 1/m).

(%i5) pdf_exp(x, m);
                                - m x
(%o5)                       m %e      unit_step(x)

cdf_exp (x, m)
Returns the value at x of the distribution function of an Exponential(m) random variable, with m > 0.

(%i6) cdf_exp(x, m);
                                 - m x
(%o6)                     (1 - %e     ) unit_step(x)

quantile_exp (q, m)
Returns the q-quantile of an Exponential(m) random variable, with m > 0; in other words, this is the inverse of cdf_exp. Argument q must be an element of [0, 1].

(%i7) quantile_exp(0.56, 5);
(%o7)                         0.1641961104139661
(%i8) quantile_exp(0.56, m);
                              0.8209805520698303
(%o8)                         ------------------
                                      m

mean_exp (m)
Returns the mean of an Exponential(m) random variable, with m > 0.

(%i9) mean_exp(m);
                                       1
(%o9)                                  -
                                       m

var_exp (m)
Returns the variance of an Exponential(m) random variable, with m > 0.

(%i10) var_exp(m);
                                      1
(%o10)                                --
                                       2
                                      m

std_exp (m)
Returns the standard deviation of an Exponential(m) random variable, with m > 0.

(%i11) std_exp(m);
                                       1
(%o11)                                 -
                                       m

skewness_exp (m)
Returns the skewness coefficient of an Exponential(m) random variable, with m > 0.

(%i12) skewness_exp(m);
(%o12)                                 2

kurtosis_exp (m)
Returns the kurtosis coefficient of an Exponential(m) random variable, with m > 0.

(%i13) kurtosis_exp(m);
(%o13)                                 6

random_exp (m)
random_exp (m, k)
Returns an Exponential(m) random variate, with m > 0. Calling random_exp with a second argument k, a random sample of size k will be simulated. The simulation algorithm is based on the general inverse method.

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