Solving function containing gamma in Python

Question

I'm quite new to programming with python.

I was wondering, if there is a smart way to solve a function, which includes a gamma function with a certain shape and scale.

I already created a function G(x), which is the cdf of a gamma function up to a variable x. Now I want to solve another function including G(x). It should look like: 0=x+2*G(x)-b. Where b is a constant.

My code looks like that:

b= 10

def G(x): 
  return gamma.cdf(x,a=4,scale=25)

f = solve(x+2*G(x)-b,x,dict=True)

How is it possible to get a real value for G(x) in my solve function?

Thanks in advance!

Answer 1

To get roots from a function there are several tools in the scipy module.

Here is a solution with the method fsolve()

from scipy.stats import gamma
from scipy.optimize import fsolve

def G(x): 
  return gamma.cdf(x,a=4,scale=25)

# we define the function to solve
def f(x,b):
  return x+2*G(x)-b

b = 10
init = 0. # The starting estimate for the roots of f(x) = 0.
roots = fsolve(f,init,args=(b))

print roots

Gives output:

[9.99844838]

Given that G(10) is close to zero this solution seems likely

Sorry, I didn't take into account your dict=True option but I guess you are able to put the result in whatever structure you want without my help.

Answer 2

rom sympy import *
# from scipy.stats import gamma
# from sympy.stats import Arcsin, density, cdf
x, y, z, t, gamma, cdf = symbols('x y z t gamma cdf')

#sol = solve([x - 3, y - 1], dict=True)

from sympy.stats import Cauchy, density
from sympy import Symbol
x0 = Symbol("x0")
gamma = Symbol("gamma", positive=True)
z = Symbol("z")
X = Cauchy("x", x0, gamma)
density(X)(z)
print(density(X)(z))

sol = solve([x+2*density(X)(z)-10, y ], dict=True)
print(sol)

Or:

from scipy.stats import gamma
from sympy import solve, Poly, Eq, Function, exp
from sympy.abc import x, y, z, a, b

def G(x): 
  return gamma.cdf(x,a=4,scale=25)

b= 10

f = solve(x+2*G(x)-b,x,dict=True)

stats cdf gamma solve sympy