Beta

[3]:
# Parameters
func_name = "Beta"
positive_prior = True

Description

[5]:
func.display()
  • description: A beta distribution function
  • formula: $ f(x, a, b)=\frac{\Gamma(a+b) x^{a-1}(1-x)^{b-1}}{\Gamma(a) \Gamma(b)}$
  • parameters:
    • a:
      • value: 0.5
      • desc: first shape parameter
      • min_value: 0.0
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.05
      • free: True
    • b:
      • value: 0.5
      • desc: second shape parameter
      • min_value: 0.0
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.05
      • free: True

Shape

The shape of the function.

If this is not a photon model but a prior or linear function then ignore the units as these docs are auto-generated

[6]:
fig, ax = plt.subplots()


ax.plot(energy_grid, func(energy_grid), color=blue, lw=3)

ax.set_xlabel("x")
ax.set_ylabel("probability")

[6]:
Text(0, 0.5, 'probability')
../_images/notebooks_Beta_8_1.png

Random Number Generation

This is how we can generate random numbers from the prior.

[7]:


u = np.random.uniform(0,1, size=5000) draws = [func.from_unit_cube(x) for x in u] fig, ax = plt.subplots() ax.hist(draws, color=green, bins=50) ax.set_xlabel("value") ax.set_ylabel("N")

[7]:
Text(0, 0.5, 'N')
../_images/notebooks_Beta_10_1.png