:py:mod:`ler.gw_source_population.powerlaw_plus_peak`
=====================================================

.. py:module:: ler.gw_source_population.powerlaw_plus_peak


Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   ler.gw_source_population.powerlaw_plus_peak.powerlaw_plus_peak_unnormalized
   ler.gw_source_population.powerlaw_plus_peak.powerlaw_plus_peak_pdf
   ler.gw_source_population.powerlaw_plus_peak.powerlaw_plus_peak_cdf
   ler.gw_source_population.powerlaw_plus_peak.powerlaw_plus_peak_function
   ler.gw_source_population.powerlaw_plus_peak.powerlaw_plus_peak_rvs



.. py:function:: powerlaw_plus_peak_unnormalized(m, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.003, delta_m=4.8)

   
   Compute unnormalized PDF for power-law + Gaussian model.

   Evaluates the unnormalized mixture of power-law and Gaussian distributions
   with low-mass smoothing applied, prior to normalization.

   :Parameters:

       **m** : ``numpy.ndarray``
           Mass values (solar masses).

       **mminbh** : ``float``
           Minimum BH mass (solar masses).

       **mmaxbh** : ``float``
           Maximum BH mass (solar masses).

       **alpha** : ``float``
           Power-law spectral index.

       **mu_g** : ``float``
           Mean of Gaussian peak (solar masses).

       **sigma_g** : ``float``
           Standard deviation of Gaussian peak (solar masses).

       **lambda_peak** : ``float``
           Fraction in Gaussian component (0-1).

       **delta_m** : ``float``
           Smoothing width (solar masses).



   :Returns:

       **density** : ``numpy.ndarray``
           Unnormalized probability density values.











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.. py:function:: powerlaw_plus_peak_pdf(m, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.003, delta_m=4.8, normalization_size=500)

   
   Evaluate fully normalized primary-mass probability density (power-law + Gaussian model).

   Computes the normalized PDF combining a power-law distribution with a single
   Gaussian peak for black hole primary masses.

   :Parameters:

       **m** : ``numpy.ndarray``
           Mass values to evaluate (solar masses).

       **mminbh** : ``float``
           Minimum BH mass (solar masses).

       **mmaxbh** : ``float``
           Maximum BH mass (solar masses).

       **alpha** : ``float``
           Power-law spectral index for the power-law component.

       **mu_g** : ``float``
           Mean of the Gaussian peak (solar masses).

       **sigma_g** : ``float``
           Standard deviation of the Gaussian peak (solar masses).

       **lambda_peak** : ``float``
           Fraction of sources in the Gaussian component (0-1).

       **delta_m** : ``float``
           Low-mass smoothing width (solar masses).

       **normalization_size** : ``int``
           Grid size for normalization.
           default: 500



   :Returns:

       **pdf** : ``numpy.ndarray``
           Normalized probability density values.










   .. rubric:: Examples

   >>> from ler.gw_source_population.prior_functions import powerlaw_plus_peak_pdf
   >>> import numpy as np
   >>> m = np.array([20.0, 40.0, 60.0])
   >>> pdf_values = powerlaw_plus_peak_pdf(m, mminbh=5, mmaxbh=100, alpha=2.3, mu_g=50, sigma_g=10, lambda_peak=0.1, delta_m=5)
   >>> print(pdf_values)  # doctest: +SKIP

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.. py:function:: powerlaw_plus_peak_cdf(size, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.003, delta_m=4.8)

   
   Compute cumulative distribution function for power-law + Gaussian mass model.

   Evaluates the CDF using numerical integration for primary mass distribution.

   :Parameters:

       **size** : ``int``
           Number of grid points for CDF computation.

       **mminbh** : ``float``
           Minimum BH mass (solar masses).

       **mmaxbh** : ``float``
           Maximum BH mass (solar masses).

       **alpha** : ``float``
           Power-law spectral index.

       **mu_g** : ``float``
           Mean of the Gaussian peak (solar masses).

       **sigma_g** : ``float``
           Standard deviation of the Gaussian peak (solar masses).

       **lambda_peak** : ``float``
           Fraction in Gaussian component (0-1).

       **delta_m** : ``float``
           Low-mass smoothing width (solar masses).



   :Returns:

       **cdf_values** : ``numpy.ndarray``
           Normalized CDF values at each grid point.











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.. py:function:: powerlaw_plus_peak_function(m, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.003, delta_m=4.8, normalization_size=500, R0=16.158, kappa=3.166, z_eval=0.2)

   
   Evaluate the redshift-dependent merger rate density for the power-law + Gaussian mass model.
   Combines the normalized mass distribution with a redshift evolution model to compute the merger rate density as a function of mass and redshift.


   :Parameters:

       **m** : ``numpy.ndarray``
           Mass values to evaluate (solar masses).

       **mminbh** : ``float``
           Minimum BH mass (solar masses).

       **mmaxbh** : ``float``
           Maximum BH mass (solar masses).

       **alpha** : ``float``
           Power-law spectral index for the mass distribution.

       **mu_g** : ``float``
           Mean of the Gaussian peak (solar masses).

       **sigma_g** : ``float``
           Standard deviation of the Gaussian peak (solar masses).

       **lambda_peak** : ``float``
           Fraction of sources in the Gaussian component (0-1).

       **delta_m** : ``float``
           Low-mass smoothing width (solar masses).

       **normalization_size** : ``int``
           Grid size for normalization of the mass distribution.
           default: 500

       **R0** : ``float``
           Local merger rate density at z=0 (Gpc^-3 yr^-1).
           default: 16.158

       **kappa** : ``float``
           Power-law index for redshift evolution of the merger rate.
           default: 3.166

       **z_eval** : ``float``
           Redshift at which to evaluate the merger rate density.
           default: 0.2



   :Returns:

       **rate_density** : ``numpy.ndarray``
           Merger rate density as a function of mass at the specified redshift (Gpc^-3 yr^-1 Msun^-1).











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.. py:function:: powerlaw_plus_peak_rvs(size, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.003, delta_m=4.8, normalization_size=500)

   
   Generate random samples from the power-law + Gaussian mass distribution.


   :Parameters:

       **size** : ``int``
           Number of samples to draw.

       **mminbh** : ``float``
           Minimum BH mass (solar masses).

       **mmaxbh** : ``float``
           Maximum BH mass (solar masses).

       **alpha** : ``float``
           Power-law spectral index for the power-law component.

       **mu_g** : ``float``
           Mean of the Gaussian peak (solar masses).

       **sigma_g** : ``float``
           Standard deviation of the Gaussian peak (solar masses).

       **lambda_peak** : ``float``
           Fraction of sources in the Gaussian component (0-1).

       **delta_m** : ``float``
           Low-mass smoothing width (solar masses).

       **normalization_size** : ``int``
           Grid size for CDF computation.
           default: 500



   :Returns:

       **samples** : ``numpy.ndarray``
           Mass samples drawn from the specified distribution (solar masses).











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