Basic PDFs

Basic shapes are fundamendal PDFs, with often well-known functional form. They are usually fully analytically implemented and often a thin wrapper around Distribution. Any missing shape can be easily wrapped using WrapDistribution.

Below are visualizations of some common PDFs with different parameter values to help understand their shapes and choose appropriate initial parameter values.

Gaussian PDF

The Gauss (or Normal) distribution is characterized by its mean (mu) and standard deviation (sigma).

zfit.pdf.Gauss(mu, sigma, obs, *[, ...])

Gaussian or Normal distribution with a mean (mu) and a standard deviation (sigma).

Exponential PDF

The Exponential distribution is characterized by its decay parameter (lambda).

zfit.pdf.Exponential([lam, obs, extended, ...])

Exponential function exp(lambda * x).

Uniform PDF

The Uniform distribution is characterized by its lower and upper bounds.

zfit.pdf.Uniform(low, high, obs, *[, ...])

Uniform distribution which is constant between low, high and zero outside.

Cauchy PDF

The Cauchy distribution is characterized by its location parameter (m) and scale parameter (gamma).

zfit.pdf.Cauchy(m, gamma, obs, *[, ...])

Non-relativistic Breit-Wigner (Cauchy) PDF representing the energy distribution of a decaying particle.

Voigt PDF

The Voigt profile is a convolution of a Gaussian and a Lorentzian distribution.

zfit.pdf.Voigt(m, sigma, gamma[, obs, ...])

Voigt profile.

CrystalBall PDF

The CrystalBall function is a Gaussian with a power-law tail.

zfit.pdf.CrystalBall(mu, sigma, alpha, n, obs, *)

Crystal Ball shaped PDF.

LogNormal PDF

The LogNormal distribution is the distribution of a random variable whose logarithm follows a normal distribution.

zfit.pdf.LogNormal(mu, sigma, obs, *[, ...])

Log-normal distribution, the exponential of a normal distribution.

ChiSquared PDF

The ChiSquared distribution is the distribution of a sum of the squares of k independent standard normal random variables.

zfit.pdf.ChiSquared(ndof, obs, *[, ...])

ChiSquared distribution for ndof degrees of freedom.

StudentT PDF

The StudentT t-distribution is a continuous probability distribution that generalizes the normal distribution.

zfit.pdf.StudentT(ndof, mu, sigma, obs[, ...])

StudentT distribution for ndof degrees of freedom.

Gamma PDF

The Gamma distribution is a two-parameter family of continuous probability distributions.

zfit.pdf.Gamma(gamma, beta, mu, obs, *[, ...])

Gamma distribution.

BifurGauss PDF

The BifurGauss distribution is a Gaussian with different widths on the left and right sides.

zfit.pdf.BifurGauss(mu, sigmal, sigmar, obs, *)

Bifurcated Gaussian distribution different standard deviations for the left and right side of the mean.

Poisson PDF

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

zfit.pdf.Poisson([lam, obs, extended, norm, ...])

Poisson distribution, parametrized with an event rate parameter (lamb).

QGauss PDF

The QGauss distribution is a q-Gaussian distribution, which is a generalization of the normal distribution.

zfit.pdf.QGauss(q, mu, sigma, obs, *[, ...])

Q-Gaussian distribution with parameter q.

JohnsonSU PDF

The JohnsonSU distribution is a four-parameter family of probability distributions.

zfit.pdf.JohnsonSU(mu, lambd, gamma, delta, ...)

Johnson's SU distribution.

GeneralizedGauss PDF

The GeneralizedGauss distribution is a generalization of the normal distribution with an additional shape parameter.

zfit.pdf.GeneralizedGauss(mu, sigma, beta, ...)

Generalized Gaussian distribution with a mean (mu), a standard deviation (sigma), and a shape parameter (beta).

TruncatedGauss PDF

The TruncatedGauss distribution is a Gaussian distribution that is truncated to a specified range.

zfit.pdf.TruncatedGauss(mu, sigma, low, ...)

Gaussian distribution that is 0 outside of low, high.

ExpModGauss PDF

The ExpModGauss distribution is a Gaussian distribution convolved with an exponential distribution.

zfit.pdf.ExpModGauss(mu, sigma, lambd, obs, *)

Exponentially modified Gaussian distribution with a mean (mu), a standard deviation (sigma), and an exponential rate parameter (lambd).

Beta PDF

The Beta distribution is defined on the interval [0, 1] and is characterized by two shape parameters alpha and beta.

zfit.pdf.Beta(alpha, beta, obs, *[, ...])

Beta distribution with shape parameters alpha and beta.

zfit.pdf.Gauss(mu, sigma, obs, *[, ...])	Gaussian or Normal distribution with a mean (mu) and a standard deviation (sigma).
zfit.pdf.Exponential([lam, obs, extended, ...])	Exponential function exp(lambda * x).
zfit.pdf.CrystalBall(mu, sigma, alpha, n, obs, *)	Crystal Ball shaped PDF.
zfit.pdf.DoubleCB(mu, sigma, alphal, nl, ...)	Double-sided Crystal Ball shaped PDF.
zfit.pdf.GeneralizedCB(mu, sigmal, alphal, ...)	Generalized asymmetric double-sided Crystal Ball shaped PDF.
zfit.pdf.GaussExpTail(mu, sigma, alpha, obs, *)	GaussExpTail shaped PDF.
zfit.pdf.GeneralizedGaussExpTail(mu, sigmal, ...)	GeneralizedGaussedExpTail shaped PDF which is Generalized assymetric double-sided GaussExpTail shaped PDF.
zfit.pdf.Uniform(low, high, obs, *[, ...])	Uniform distribution which is constant between low, high and zero outside.
zfit.pdf.Cauchy(m, gamma, obs, *[, ...])	Non-relativistic Breit-Wigner (Cauchy) PDF representing the energy distribution of a decaying particle.
zfit.pdf.Voigt(m, sigma, gamma[, obs, ...])	Voigt profile.
zfit.pdf.TruncatedGauss(mu, sigma, low, ...)	Gaussian distribution that is 0 outside of low, high.
zfit.pdf.BifurGauss(mu, sigmal, sigmar, obs, *)	Bifurcated Gaussian distribution different standard deviations for the left and right side of the mean.
zfit.pdf.Poisson([lam, obs, extended, norm, ...])	Poisson distribution, parametrized with an event rate parameter (lamb).
zfit.pdf.LogNormal(mu, sigma, obs, *[, ...])	Log-normal distribution, the exponential of a normal distribution.
zfit.pdf.QGauss(q, mu, sigma, obs, *[, ...])	Q-Gaussian distribution with parameter q.
zfit.pdf.ChiSquared(ndof, obs, *[, ...])	ChiSquared distribution for ndof degrees of freedom.
zfit.pdf.StudentT(ndof, mu, sigma, obs[, ...])	StudentT distribution for ndof degrees of freedom.
zfit.pdf.Gamma(gamma, beta, mu, obs, *[, ...])	Gamma distribution.
zfit.pdf.JohnsonSU(mu, lambd, gamma, delta, ...)	Johnson's SU distribution.
zfit.pdf.GeneralizedGauss(mu, sigma, beta, ...)	Generalized Gaussian distribution with a mean (mu), a standard deviation (sigma), and a shape parameter (beta).
zfit.pdf.ExpModGauss(mu, sigma, lambd, obs, *)	Exponentially modified Gaussian distribution with a mean (mu), a standard deviation (sigma), and an exponential rate parameter (lambd).
zfit.pdf.Beta(alpha, beta, obs, *[, ...])	Beta distribution with shape parameters alpha and beta.