<p>你的问题也有其他选择。Wikipedia有一个<a href="https://en.wikipedia.org/wiki/List_of_probability_distributions#Supported_on_a_bounded_interval" rel="nofollow noreferrer">continuous distributions with bounded intervals</a>的列表,这取决于分布,您可以使用正确的参数获得所需的特性。例如,如果您想要类似“有界高斯铃”(不截断)的内容,可以选择(缩放的)<a href="https://en.wikipedia.org/wiki/Beta_distribution" rel="nofollow noreferrer">beta distribution</a>:</p>
<pre><code>import numpy as np
import scipy.stats
import matplotlib.pyplot as plt
def my_distribution(min_val, max_val, mean, std):
scale = max_val - min_val
location = min_val
# Mean and standard deviation of the unscaled beta distribution
unscaled_mean = (mean - min_val) / scale
unscaled_var = (std / scale) ** 2
# Computation of alpha and beta can be derived from mean and variance formulas
t = unscaled_mean / (1 - unscaled_mean)
beta = ((t / unscaled_var) - (t * t) - (2 * t) - 1) / ((t * t * t) + (3 * t * t) + (3 * t) + 1)
alpha = beta * t
# Not all parameters may produce a valid distribution
if alpha <= 0 or beta <= 0:
raise ValueError('Cannot create distribution for the given parameters.')
# Make scaled beta distribution with computed parameters
return scipy.stats.beta(alpha, beta, scale=scale, loc=location)
np.random.seed(100)
min_val = 1.5
max_val = 35
mean = 9.87
std = 3.1
my_dist = my_distribution(min_val, max_val, mean, std)
# Plot distribution PDF
x = np.linspace(min_val, max_val, 100)
plt.plot(x, my_dist.pdf(x))
# Stats
print('mean:', my_dist.mean(), 'std:', my_dist.std())
# Get a large sample to check bounds
sample = my_dist.rvs(size=100000)
print('min:', sample.min(), 'max:', sample.max())
</code></pre>
<p>输出:</p>
<pre class="lang-none prettyprint-override"><code>mean: 9.87 std: 3.100000000000001
min: 1.9290674232087306 max: 25.03903889816994
</code></pre>
<p>概率密度函数图:</p>
<p><a href="https://i.stack.imgur.com/MzOwi.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/MzOwi.png" alt="Probability density function"/></a></p>
<p>注意,在这种情况下,并不是所有可能的界限、平均值和标准差的组合都会产生一个有效的分布,并且取决于<code>alpha</code>和<code>beta</code>的结果值,概率密度函数可能看起来像一个“倒钟”(即使平均值和标准差仍然是正确的)。</p>