Generate random numbers with a given (numerical) distribution



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%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



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from scipy.stats import norm

Theoretical distribution

With mean 50 and standard deviation 10



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# Create a normal distribution
mu = 50
sigma = 10 # standard deviation
rv = norm(loc = mu, scale = sigma)

start = rv.ppf(0.00001)

stop  = rv.ppf(0.99999)
x = np.linspace(start, stop, 100)

print(start, stop)
plt.plot(x, rv.pdf(x))
plt.xlabel('Cells IDs'), plt.ylabel('Conductance');
plt.xlim(0,100);









    



(7.3510920607717551, 92.648907939238399)

Empirical distribution



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# generate empirical distribution
cell_idx = np.arange(int(start), int(stop))
mycond = [rv.pdf(i) for i in cell_idx]
print(mycond[50])









    



0.0312253933367



In [9]:

    
plt.bar( cell_idx, mycond, width=.85, facecolor='k', label='empirical');
plt.xlabel('Cells IDs'), plt.ylabel('Conductance');

note that cells with ID <12 or > 87 receive almost zero conductance (check sigma)



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rv.pdf(87)









    Out[10]:





4.2478027055075142e-05

Plot both together



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plt.plot(x, rv.pdf(x), c='r')
plt.bar( cell_idx, mycond, width=.85, facecolor='k', label='empirical');
plt.xlabel('Cells IDs'), plt.ylabel('Conductance');

let's generate another distribution with mean = 0 and standar deviation of 10



In [13]:

    
rv2 = norm(loc = 0, scale = 10)
start = rv2.ppf(0.0001)
stop  = rv2.ppf(0.9999)
x = np.linspace(start, stop, 100)

mycond = [rv2.pdf(i) for i in x]
print(start, stop)









    



(-37.190164854556805, 37.190164854557089)



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cell_idx = np.arange(int(start), int(stop))
mycond = [rv2.pdf(i) for i in cell_idx]

plt.plot(x, rv2.pdf(x), color = 'red')
plt.bar( cell_idx, mycond, width=.85, facecolor='k', label='empirical');
plt.xlabel('Cells IDs'), plt.ylabel('Conductance');



In [22]:

    
rv3 = norm(loc = 0, scale = 20)
start = rv3.ppf(0.0001)
stop  = rv3.ppf(0.9999)

x = np.arange(start, stop)
plt.plot(x, rv3.pdf(x)/10, 'red')

print(start, stop)









    



(-74.38032970911361, 74.380329709114179)



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