Cauchy

[3]:
# Parameters
func_name = "Cauchy"
wide_energy_range = True
x_scale = "linear"
y_scale = "linear"
linear_range = True

Description

[5]:
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)

ax.set_xlabel("energy (keV)")
ax.set_ylabel("photon flux")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

../_images/notebooks_Cauchy_8_0.png

F\(_{\nu}\)

The F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[7]:
fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid * func(energy_grid), red)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"energy flux (F$_{\nu}$)")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)


../_images/notebooks_Cauchy_10_0.png

\(\nu\)F\(_{\nu}\)

The \(\nu\)F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[8]:
fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid**2 * func(energy_grid), color=green)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"$\nu$F$_{\nu}$")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

../_images/notebooks_Cauchy_12_0.png