Planck-Tapered Broken Power Law Plus Two Peaks

planck_tapered_broken_power_law_plus_two_peaks ¶

Broken power law plus two peaks distribution with Planck tapering.

Functions¶

planck_tapered_broken_power_law_plus_two_peaks_unnormalized_logpdf ¶

planck_tapered_broken_power_law_plus_two_peaks_unnormalized_logpdf(x: Array, alpha_1: float, alpha_2: float, transition: float, minimum: float, maximum: float, mean_1: float, sigma_1: float, mean_2: float, sigma_2: float, taper_range: float, lambda_0: float, lambda_1: float) -> Array

Compute the unnormalized logpdf of Planck tapered broken power law plus two peaks distribution.

Parameters:

Name	Type	Description	Default
`x`	`Array`	An array of values to evaluate the unnormalized pdf.	required
`alpha_1`	`float`	Spectral index of the first power law.	required
`alpha_2`	`float`	Spectral index of the second power law.	required
`transition`	`float`	Transition point of the broken power law.	required
`minimum`	`float`	Minimum of the distribution.	required
`maximum`	`float`	Maximum of the distribution.	required
`mean_1`	`float`	Mean of the first peak.	required
`sigma_1`	`float`	Standard deviation of the first peak.	required
`mean_2`	`float`	Mean of the second peak.	required
`sigma_2`	`float`	Standard deviation of the second peak.	required
`taper_range`	`float`	Range of the tapering.	required
`lambda_0`	`float`	Mixing fraction of the power law.	required
`lambda_1`	`float`	Mixing fraction of the first peak.	required

Returns:

Type	Description
`Array`	Unnormalized logpdf.

planck_tapered_broken_power_law_plus_two_peaks_cdf ¶

planck_tapered_broken_power_law_plus_two_peaks_cdf(alpha_1: float, alpha_2: float, transition: float, minimum: float, maximum: float, mean_1: float, sigma_1: float, mean_2: float, sigma_2: float, taper_range: float, lambda_0: float, lambda_1: float, n_grids: int) -> tuple[Array, Array]

Compute the cdf of Planck tapered broken power law plus two peaks distribution.

Parameters:

Name	Type	Description	Default
`alpha_1`	`float`	Spectral index of the first power law.	required
`alpha_2`	`float`	Spectral index of the second power law.	required
`transition`	`float`	Transition point of the broken power law.	required
`minimum`	`float`	Minimum of the distribution.	required
`maximum`	`float`	Maximum of the distribution.	required
`mean_1`	`float`	Mean of the first peak.	required
`sigma_1`	`float`	Standard deviation of the first peak.	required
`mean_2`	`float`	Mean of the second peak.	required
`sigma_2`	`float`	Standard deviation of the second peak.	required
`taper_range`	`float`	Range of the tapering.	required
`lambda_0`	`float`	Mixing fraction of the power law.	required
`lambda_1`	`float`	Mixing fraction of the first peak.	required
`n_grids`	`int`	Number of grid points to evaluate the CDF.	required

Returns:

Name	Type	Description
`x`	`Array`	Grid points to evaluate the CDF.
`cdf`	`Array`	Cumulative distribution function.