diff options
Diffstat (limited to 'Lib/random.py')
| -rw-r--r-- | Lib/random.py | 39 |
1 files changed, 34 insertions, 5 deletions
diff --git a/Lib/random.py b/Lib/random.py index 84bbfc5..1d789b1 100644 --- a/Lib/random.py +++ b/Lib/random.py @@ -492,7 +492,14 @@ class Random(_random.Random): ## -------------------- real-valued distributions ------------------- def uniform(self, a, b): - "Get a random number in the range [a, b) or [a, b] depending on rounding." + """Get a random number in the range [a, b) or [a, b] depending on rounding. + + The mean (expected value) and variance of the random variable are: + + E[X] = (a + b) / 2 + Var[X] = (b - a) ** 2 / 12 + + """ return a + (b - a) * self.random() def triangular(self, low=0.0, high=1.0, mode=None): @@ -503,6 +510,11 @@ class Random(_random.Random): http://en.wikipedia.org/wiki/Triangular_distribution + The mean (expected value) and variance of the random variable are: + + E[X] = (low + high + mode) / 3 + Var[X] = (low**2 + high**2 + mode**2 - low*high - low*mode - high*mode) / 18 + """ u = self.random() try: @@ -593,12 +605,15 @@ class Random(_random.Random): positive infinity if lambd is positive, and from negative infinity to 0 if lambd is negative. - """ - # lambd: rate lambd = 1/mean - # ('lambda' is a Python reserved word) + The mean (expected value) and variance of the random variable are: + + E[X] = 1 / lambd + Var[X] = 1 / lambd ** 2 + """ # we use 1-random() instead of random() to preclude the # possibility of taking the log of zero. + return -_log(1.0 - self.random()) / lambd def vonmisesvariate(self, mu, kappa): @@ -654,8 +669,12 @@ class Random(_random.Random): pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha + The mean (expected value) and variance of the random variable are: + + E[X] = alpha * beta + Var[X] = alpha * beta ** 2 + """ - # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 # Warning: a few older sources define the gamma distribution in terms # of alpha > -1.0 @@ -714,6 +733,11 @@ class Random(_random.Random): Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. + The mean (expected value) and variance of the random variable are: + + E[X] = alpha / (alpha + beta) + Var[X] = alpha * beta / ((alpha + beta)**2 * (alpha + beta + 1)) + """ ## See ## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html @@ -766,6 +790,11 @@ class Random(_random.Random): Returns an integer in the range: 0 <= X <= n + The mean (expected value) and variance of the random variable are: + + E[X] = n * p + Var[x] = n * p * (1 - p) + """ # Error check inputs and handle edge cases if n < 0: |