# Fit_Gamma_3P¶

class reliability.Fitters.Fit_Gamma_3P(failures=None, right_censored=None, show_probability_plot=True, print_results=True, CI=0.95, optimizer=None, method='MLE', percentiles=None, CI_type='time', **kwargs)

Fits a 3-parameter Gamma distribution (alpha,beta,gamma) to the data provided. You may also enter right censored data.

Inputs: failures - an array or list of failure data right_censored - an array or list of right censored data show_probability_plot - True/False. Defaults to True. print_results - True/False. Defaults to True. Prints a dataframe of the point estimate, standard error, Lower CI and Upper CI for each parameter. CI - confidence interval for estimating confidence limits on parameters. Must be between 0 and 1. Default is 0.95 for 95% CI. CI_type - time, reliability, None. Default is time. This is the confidence bounds on time or on reliability. Use None to turn off the confidence intervals. percentiles - percentiles to produce a table of percentiles failed with lower, point, and upper estimates. Default is None which results in no output. True or ‘auto’ will use default array [1, 5, 10,…, 95, 99]. If an array or list is specified then it will be used instead of the default array. method - ‘MLE’ (maximum likelihood estimation), or ‘LS’ (least squares estimation). LS will perform non-linear least squares estimation. Default is ‘MLE’. optimizer - ‘L-BFGS-B’, ‘TNC’, or ‘powell’. These are all bound constrained methods. If the bounded method fails, nelder-mead will be used. If nelder-mead fails then the initial guess will be returned with a warning. For more information on optimizers see https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize kwargs are accepted for the probability plot (eg. linestyle, label, color)

Outputs: alpha - the fitted Gamma_3P alpha parameter beta - the fitted Gamma_3P beta parameter gamma - the fitted Gamma_3P gamma parameter loglik - Log Likelihood (as used in Minitab and Reliasoft) loglik2 - LogLikelihood*-2 (as used in JMP Pro) AICc - Akaike Information Criterion BIC - Bayesian Information Criterion AD - the Anderson Darling (corrected) statistic (as reported by Minitab) distribution - a Gamma_Distribution object with the parameters of the fitted distribution alpha_SE - the standard error (sqrt(variance)) of the parameter beta_SE - the standard error (sqrt(variance)) of the parameter gamma_SE - the standard error (sqrt(variance)) of the parameter alpha_upper - the upper CI estimate of the parameter alpha_lower - the lower CI estimate of the parameter beta_upper - the upper CI estimate of the parameter beta_lower - the lower CI estimate of the parameter gamma_upper - the upper CI estimate of the parameter gamma_lower - the lower CI estimate of the parameter results - a dataframe of the results (point estimate, standard error, Lower CI and Upper CI for each parameter) goodness_of_fit - a dataframe of the goodness of fit values (Log-likelihood, AICc, BIC, AD). percentiles - a dataframe of the percentiles with bounds on time. This is only produced if percentiles is ‘auto’ or a list or array. Since percentiles defaults to None, this output is not normally produced. probability_plot - the axes handle for the probability plot (only returned if show_probability_plot = True)

static LL(params, T_f, T_rc)
static logR(t, a, b, g)
static logf(t, a, b, g)