Cómo generar una distribución normal aleatoria de enteros.

Otra forma posible de obtener una distribución discreta que se parece a la distribución normal es recurrir a una distribución multinomial donde las probabilidades se calculan a partir de una distribución normal.

 import scipy.stats as ss import numpy as np import matplotlib.pyplot as plt x = np.arange(-10, 11) xU, xL = x + 0.5, x - 0.5 prob = ss.norm.cdf(xU, scale = 3) - ss.norm.cdf(xL, scale = 3) prob = prob / prob.sum() #normalize the probabilities so their sum is 1 nums = np.random.choice(x, size = 10000, p = prob) plt.hist(nums, bins = len(x)) 

Aquí, np.random.choice elige un número entero de [-10, 10]. La probabilidad de seleccionar un elemento, digamos 0, se calcula mediante p (-0.5

El resultado se ve así:

Puede ser posible generar una distribución similar a partir de una distribución normal truncada que se redondea a números enteros. Aquí hay un ejemplo con truncnorm de Scipy () .

 import numpy as np from scipy.stats import truncnorm import matplotlib.pyplot as plt scale = 3. range = 10 size = 100000 X = truncnorm(a=-range/scale, b=+range/scale, scale=scale).rvs(size=size) X = X.round().astype(int) 

Veamos como se ve

 bins = 2 * range + 1 plt.hist(X, bins) 

Aquí empezamos por obtener valores de la curva de campana .

CÓDIGO:

 #--------*---------*---------*---------*---------*---------*---------*---------* # Desc: Discretize a normal distribution centered at 0 #--------*---------*---------*---------*---------*---------*---------*---------* import sys import random from math import sqrt, pi import numpy as np import matplotlib.pyplot as plt def gaussian(x, var): k1 = np.power(x, 2) k2 = -k1/(2*var) return (1./(sqrt(2. * pi * var))) * np.exp(k2) #--------*---------*---------*---------*---------*---------*---------*---------# while 1:# MAINLINE # #--------*---------*---------*---------*---------*---------*---------*---------# # # probability density function # # for discrete normal RV pdf_DGV = [] pdf_DGW = [] var = 9 tot = 0 # # create 'rough' gaussian for i in range(-var - 1, var + 2): if i == -var - 1: r_pdf = + gaussian(i, 9) + gaussian(i - 1, 9) + gaussian(i - 2, 9) elif i == var + 1: r_pdf = + gaussian(i, 9) + gaussian(i + 1, 9) + gaussian(i + 2, 9) else: r_pdf = gaussian(i, 9) tot = tot + r_pdf pdf_DGV.append(i) pdf_DGW.append(r_pdf) print(i, r_pdf) # # amusing how close tot is to 1! print('\nRough total = ', tot) # # no need to normalize with Python 3.6, # # but can't help ourselves for i in range(0,len(pdf_DGW)): pdf_DGW[i] = pdf_DGW[i]/tot # # print out pdf weights # # for out discrte gaussian print('\npdf:\n') print(pdf_DGW) # # plot random variable action rv_samples = random.choices(pdf_DGV, pdf_DGW, k=10000) plt.hist(rv_samples, bins = 100) plt.show() sys.exit() 

SALIDA:

 -10 0.0007187932912256041 -9 0.001477282803979336 -8 0.003798662007932481 -7 0.008740629697903166 -6 0.017996988837729353 -5 0.03315904626424957 -4 0.05467002489199788 -3 0.0806569081730478 -2 0.10648266850745075 -1 0.12579440923099774 0 0.1329807601338109 1 0.12579440923099774 2 0.10648266850745075 3 0.0806569081730478 4 0.05467002489199788 5 0.03315904626424957 6 0.017996988837729353 7 0.008740629697903166 8 0.003798662007932481 9 0.001477282803979336 10 0.0007187932912256041 Rough total = 0.9999715875468381 pdf: [0.000718813714486599, 0.0014773247784004072, 0.003798769940305483, 0.008740878047691289, 0.017997500190860556, 0.033159988420867426, 0.05467157824565407, 0.08065919989878699, 0.10648569402724471, 0.12579798346031068, 0.13298453855078374, 0.12579798346031068, 0.10648569402724471, 0.08065919989878699, 0.05467157824565407, 0.033159988420867426, 0.017997500190860556, 0.008740878047691289, 0.003798769940305483, 0.0014773247784004072, 0.000718813714486599] 

La respuesta aceptada aquí funciona, pero probé la solución de Will Vousden y también funciona bien:

 import numpy as np # Generate Distribution: randomNums = np.random.normal(scale=3, size=100000) randomInts = np.round(randomNums) # Plot: axis = np.arange(start=min(randomInts), stop = max(randomInts) + 1) plt.hist(randomInts, bins = axis)