Truncated gaussian

# Parameters
func_name = "Truncated_gaussian"
positive_prior = False

Description

func.display()

• description: A truncated Gaussian function defined on the interval between the lower_bound (a) and upper_bound (b)
• formula: $\begin{split}f(x;\mu,\sigma,a,b)=\frac{\frac{1}{\sigma} \phi\left( \frac{x-\mu}{\sigma} \right)}{\Phi\left( \frac{b-\mu}{\sigma} \right) - \Phi\left( \frac{a-\mu}{\sigma} \right)}\\\phi\left(z\right)=\frac{1}{\sqrt{2 \pi}}\exp\left(-\frac{1}{2}z^2\right)\\\Phi\left(z\right)=\frac{1}{2}\left(1+erf\left(\frac{z}{\sqrt(2)}\right)\right)\end{split}$
• parameters:
  • F:
    • value: 1.0
    • desc: Integral between -inf and +inf. Fix this to 1 to obtain a Normal distribution
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • mu:
    • value: 0.0
    • desc: Central value
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • sigma:
    • value: 1.0
    • desc: standard deviation
    • min_value: 1e-12
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • lower_bound:
    • value: -1.0
    • desc: lower bound of gaussian, setting to -np.inf results in half normal distribution
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • upper_bound:
    • value: 1.0
    • desc: upper bound of gaussian setting to np.inf results in half normal distribution
    • min_value: None
    • 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')