Return samples drawn from a lognormal distribution.
Draw samples from a lognormal distribution with specified mean, standard deviation, and shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.
Parameters :  mean : float
sigma : float, >0.
size : tuple of ints


See also
Notes
A variable x has a lognormal distribution if log(x) is normally distributed.
The probability density function for the lognormal distribution is
where is the mean and is the standard deviation of the normally distributed logarithm of the variable.
A lognormal distribution results if a random variable is the product of a large number of independent, identicallydistributed variables in the same way that a normal distribution results if the variable is the sum of a large number of independent, identicallydistributed variables (see the last example). It is one of the socalled “fattailed” distributions.
The lognormal distribution is commonly used to model the lifespan of units with fatiguestress failure modes. Since this includes most mechanical systems, the lognormal distribution has widespread application.
It is also commonly used to model oil field sizes, species abundance, and latent periods of infectious diseases.
References
[R80]  Eckhard Limpert, Werner A. Stahel, and Markus Abbt, “Lognormal Distributions across the Sciences: Keys and Clues”, May 2001 Vol. 51 No. 5 BioScience http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf 
[R81]  Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme Values, Birkhauser Verlag, Basel, pp 3132. 
[R82]  Wikipedia, “Lognormal distribution”, http://en.wikipedia.org/wiki/Lognormal_distribution 
Examples
Draw samples from the distribution:
>>> mu, sigma = 3., 1. # mean and standard deviation
>>> s = np.random.lognormal(mu, sigma, 1000)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 100, normed=True, align='mid')
>>> x = np.linspace(min(bins), max(bins), 10000)
>>> pdf = (np.exp((np.log(x)  mu)**2 / (2 * sigma**2))
... / (x * sigma * np.sqrt(2 * np.pi)))
>>> plt.plot(x, pdf, linewidth=2, color='r')
>>> plt.axis('tight')
>>> plt.show()
(Source code, png, pdf)
Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a lognormal probability density function.
>>> # Generate a thousand samples: each is the product of 100 random
>>> # values, drawn from a normal distribution.
>>> b = []
>>> for i in range(1000):
... a = 10. + np.random.random(100)
... b.append(np.product(a))
>>> b = np.array(b) / np.min(b) # scale values to be positive
>>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center')
>>> sigma = np.std(np.log(b))
>>> mu = np.mean(np.log(b))
>>> x = np.linspace(min(bins), max(bins), 10000)
>>> pdf = (np.exp((np.log(x)  mu)**2 / (2 * sigma**2))
... / (x * sigma * np.sqrt(2 * np.pi)))
>>> plt.plot(x, pdf, color='r', linewidth=2)
>>> plt.show()