What is the difference between `scipy.stats.expon.rvs()` and `numpy.random.exponential()`? - numpy

Question

Simulating exponential random variables with the same mean interval time with different methods gives rise to different x axis scales
How often do we get no-hitters?
The number of games played between each no-hitter in the modern era (1901-2015) of Major League Baseball is stored in the array nohitter_times.
If you assume that no-hitters are described as a Poisson process, then the time between no-hitters is Exponentially distributed. As you have seen, the Exponential distribution has a single parameter, which we will call $τ$, the typical interval time.
The value of the parameter $τ$ that makes the exponential distribution best match the data is the mean interval time (where time is in units of number of games) between no-hitters.
# Here you go with the data
nohitter_times = np.array([ 843, 1613, 1101, 215, 684, 814, 278, 324, 161, 219, 545,
715, 966, 624, 29, 450, 107, 20, 91, 1325, 124, 1468,
104, 1309, 429, 62, 1878, 1104, 123, 251, 93, 188, 983,
166, 96, 702, 23, 524, 26, 299, 59, 39, 12, 2,
308, 1114, 813, 887, 645, 2088, 42, 2090, 11, 886, 1665,
1084, 2900, 2432, 750, 4021, 1070, 1765, 1322, 26, 548, 1525,
77, 2181, 2752, 127, 2147, 211, 41, 1575, 151, 479, 697,
557, 2267, 542, 392, 73, 603, 233, 255, 528, 397, 1529,
1023, 1194, 462, 583, 37, 943, 996, 480, 1497, 717, 224,
219, 1531, 498, 44, 288, 267, 600, 52, 269, 1086, 386,
176, 2199, 216, 54, 675, 1243, 463, 650, 171, 327, 110,
774, 509, 8, 197, 136, 12, 1124, 64, 380, 811, 232,
192, 731, 715, 226, 605, 539, 1491, 323, 240, 179, 702,
156, 82, 1397, 354, 778, 603, 1001, 385, 986, 203, 149,
576, 445, 180, 1403, 252, 675, 1351, 2983, 1568, 45, 899,
3260, 1025, 31, 100, 2055, 4043, 79, 238, 3931, 2351, 595,
110, 215, 0, 563, 206, 660, 242, 577, 179, 157, 192,
192, 1848, 792, 1693, 55, 388, 225, 1134, 1172, 1555, 31,
1582, 1044, 378, 1687, 2915, 280, 765, 2819, 511, 1521, 745,
2491, 580, 2072, 6450, 578, 745, 1075, 1103, 1549, 1520, 138,
1202, 296, 277, 351, 391, 950, 459, 62, 1056, 1128, 139,
420, 87, 71, 814, 603, 1349, 162, 1027, 783, 326, 101,
876, 381, 905, 156, 419, 239, 119, 129, 467])
First Approach:
import scipy.stats as stats
# computing the distribution parameter
avg_interval = np.mean(nohitter_times)
# Set the seed
np.random.seed(42)
# Simulating the distribution
rvs = stats.expon.rvs(avg_interval, size=100000)
#Plotting the distribution
#sns.histplot(rvs, kde=True, bins=100, color='skyblue', stat='density');
_ = plt.hist(rvs, bins=50, density=True, histtype="step")
_ = plt.xlabel('Games between no-hitters')
_ = plt.ylabel('PDF');
Second Approach:
# Seed random number generator
np.random.seed(42)
# Compute mean no-hitter time: tau
tau = np.mean(nohitter_times)
# Draw out of an exponential distribution with parameter tau: inter_nohitter_time
inter_nohitter_time = np.random.exponential(tau, 100000)
# Plot the PDF and label axes
_ = plt.hist(inter_nohitter_time, bins=50, density=True, histtype="step")
_ = plt.xlabel('Games between no-hitters')
_ = plt.ylabel('PDF')
As you can see, the two plots are totally different in terms of the x axis ticks. I don't know why?

Answer 1

I have just found out that i should have specified the scale named argument of the expon.rvs function
# computing the distribution parameter
avg_interval = np.mean(nohitter_times)
# Set the seed
np.random.seed(42)
# Simulating the distribution
rvs = stats.expon.rvs(scale=avg_interval, size=100000)
#Plotting the distribution
#sns.histplot(rvs, kde=True, bins=100, color='skyblue', stat='density');
_ = plt.hist(rvs, bins=50, density=True, histtype="step")
_ = plt.xlabel('Games between no-hitters')
_ = plt.ylabel('PDF');