# Cauchy

[3]:

# Parameters
func_name = "Cauchy"
positive_prior = False


## Description

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func.display()

• description: The Cauchy distribution
• formula: $K \frac{1}{ \gamma \pi} \left[ \frac{\gamma^2}{(x-x_0)^2 + \gamma^2} \right]$
• parameters:
• K:
• value: 1.0
• desc: Integral between -inf and +inf. Fix this to 1 to obtain a Cauchy distribution
• min_value: None
• max_value: None
• unit:
• is_normalization: False
• delta: 0.1
• free: True
• x0:
• value: 0.0
• desc: Central value
• min_value: None
• max_value: None
• unit:
• is_normalization: False
• delta: 0.1
• free: True
• gamma:
• value: 1.0
• desc: standard deviation
• min_value: 1e-12
• 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

[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')


## Random Number Generation

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

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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')