# Python np.lognormal gives infinite results for big average and St Dev

I am trying to draw the lognormal distribution for my data. using the following code :

mu, sigma = 136519., 50405. # mean and standard deviation

hs = np.random.lognormal(mu, sigma, 1000) #mean, s dev , Size

count, bins, ignored = plt.hist(hs, 100, normed=True)

x = np.linspace(min(bins), max(bins), 10000)

pdf = (math.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)))

plt.plot(x, pdf, linewidth=2, color='r')
plt.axis('tight')

As you can see, my maean and sigma are big values, it creates the problem that hs goes to infinity that gives error .

while if I put something like mu =3 and sigma =1, it works, any suggestions for big numbers?

Simply generate normal variables $x_i\sim N(136519, 50405^2)$. Numpy should be able to handle this.
Then take exponentials: $e^{x_i}$. These are on the order of $e^{150,000}$. Numpy will likely not be able to handle this. If you really need numbers on this scale, look into dedicated libraries for working with big floats.
The lognormal distribution with log-mean $\mu$ and log-SD $\sigma$ has an expected value $e^{\mu+\frac{\sigma^2}{2}}$. For the values you have, this is about as close to infinity as you are likely to get, and actual realizations will of course be much larger.