Python implementation probability distribution

1. Two-item distribution (discrete)

ImportNumPy as NP fromSciPyImportStatsImportMatplotlib.pyplot as Plt" "# Two distributions (binomial distribution) # Prerequisites: Independent repetition Test, back-up, only two results # Two distributions indicate that the probability of event A in a random experiment is p, then the probability of K event A in repeated n trials is: # f (n,k,p) = Choose (n, k) * P**k * (1-p) * * (N-K)" "#① Defining the basic information for two distributionsP = 0.4#event a probability 0.4n = 5#repeat experiment 5 timesK = Np.arange (n+1)#6 Possible results#k = Np.linspace (STATS.BINOM.PPF (0.01,n,p), STATS.BINOM.PPF (0.99,n,p), n+1) #另一种方式#② Calculating the probability mass distribution of two distributions (probability mass function)#is called mass because of discrete points, the default volume (that is, width) is 1#P (x=x)---is the probabilityProbs =STATS.BINOM.PMF (k, N, p)#Array ([0.07776, 0.2592, 0.3456, 0.2304, 0.0768, 0.01024])#Plt.plot (k, probs)#③ Calculating the cumulative probability of two distributions (cumulative density function)#P (x<=x)--and probabilityCumsum_probs =STATS.BINOM.CDF (k, N, p)#Array ([0.07776, 0.33696, 0.68256, 0.91296, 0.98976, 1. ])#④ According to the cumulative probability to get the corresponding K, here lazy, directly using the above Cumsum_probsK2 =STATS.BINOM.PPF (Cumsum_probs, N, p)#Array ([0, 1, 2, 3, 4, 5])#⑤ forgery of random variables conforming to two-item distributions (randomness variates)X = Stats.binom.rvs (n,p,size=20)#Array ([2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 3, 0, 1, 1, 1, 2, 3, 4, 0, 3])#⑧ makes the frequency histogram above that satisfies the two-item distribution random variable (similar to group by)plt.hist (X)#⑨ make a histogram of frequency distributions that meet the two distribution random variables abovePlt.hist (X, normed=True) plt.show ()

2. Normal distribution (continuous)

" "standard Normal distribution density function: f (x) = exp (-X**2/2)/sqrt (2*PI)" "x= Np.linspace (STATS.NORM.PPF (0.01), STATS.NORM.PPF (0.99), 100)#probability density distribution functions (probability density function)#This is called density because of successive points, with a default volume of 0#f (X)---not probabilityProbs =norm.pdf (x)#plt.plot (x, probs, ' R ', lw=5, alpha=0.6, label= ' Norm pdf ')#cumulative probability density functions cumulative density function#definite integral ∫_-oo^a f (x) DX----is the probabilityCumsum_probs =stats.norm.cdf (x)#forgery of random variables with normal distribution x#the LOC and scale parameters allow you to specify the offset and scaling parameters of a random variable. For random variables with normal distributions, these two parameters are equivalent to specifying their expected and standard deviations:X = Stats.norm.rvs (loc=1.0, scale=2.0, size=1000)#⑨ frequency distribution histogram of random variables with normal distribution abovePlt.hist (X, Normed=true, histtype='stepfilled', alpha=0.2) plt.legend (Loc=' Best', frameon=False) plt.show ()#parameters are estimated for the given data. It's lazy here, just use the x above.Mean, std =Stats.norm.fit (X)#Array (1.01810091), Array (2.00046946)

Python implementation probability distribution