From 8447870e721dd738bce12b45e732c9cc01dc2595 Mon Sep 17 00:00:00 2001 From: tlatorre Date: Sun, 11 Nov 2018 13:22:18 -0600 Subject: update likelihood function to fit electrons! To characterize the angular distribution of photons from an electromagnetic shower I came up with the following functional form: f(cos_theta) ~ exp(-abs(cos_theta-mu)^alpha/beta) and fit this to data simulated using RAT-PAC at several different energies. I then fit the alpha and beta coefficients as a function of energy to the functional form: alpha = c0 + c1/log(c2*T0 + c3) beta = c0 + c1/log(c2*T0 + c3). where T0 is the initial energy of the electron in MeV and c0, c1, c2, and c3 are parameters which I fit. The longitudinal distribution of the photons generated from an electromagnetic shower is described by a gamma distribution: f(x) = x**(a-1)*exp(-x/b)/(Gamma(a)*b**a). This parameterization comes from the PDG "Passage of particles through matter" section 32.5. I also fit the data from my RAT-PAC simulation, but currently I am not using it, and instead using a simpler form to calculate the coefficients from the PDG (although I estimated the b parameter from the RAT-PAC data). I also sped up the calculation of the solid angle by making a lookup table since it was taking a significant fraction of the time to compute the likelihood function. --- src/misc.c | 8 ++++++++ 1 file changed, 8 insertions(+) (limited to 'src/misc.c') diff --git a/src/misc.c b/src/misc.c index 605f3ea..d5667e8 100644 --- a/src/misc.c +++ b/src/misc.c @@ -498,3 +498,11 @@ double std(const double *x, size_t n) return sqrt(sum/n); } + +double gamma_pdf(double x, double k, double theta) +{ + /* Returns the PDF for the gamma distribution. + * + * See https://en.wikipedia.org/wiki/Gamma_distribution. */ + return pow(x,k-1)*exp(-x/theta)/(gsl_sf_gamma(k)*pow(theta,k)); +} -- cgit