Powerlaw Prior

# Parameters
func_name = "Powerlaw_Prior"
positive_prior = True

Description

func.display()

• description: An power law distribution function between a-b
• formula: $ f(x, \alpha) = \alpha x^{\alpha-1)$
• parameters:
  • alpha:
    • value: 1.0
    • desc: slope parameter
    • min_value: 0.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • a:
    • value: 0.0
    • desc: lower bound of distribution
    • min_value: 0.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • b:
    • value: 1.0
    • desc: upper bound of distribution
    • min_value: 0.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • 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

fig, ax = plt.subplots()


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

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

Text(0, 0.5, 'probability')

Random Number Generation

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

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")

Text(0, 0.5, 'N')