# Fit_Normal_2P¶

class reliability.Fitters.Fit_Normal_2P(failures=None, right_censored=None, show_probability_plot=True, print_results=True, CI=0.95, percentiles=None, optimizer=None, CI_type='time', method='MLE', force_sigma=None, **kwargs)

Fits a 2-parameter Normal distribution (mu,sigma) to the data provided. Note that it will return a fit that may be partially in the negative domain (x<0). If you need an entirely positive distribution that is similar to Normal then consider using Weibull.

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), ‘LS’ (least squares estimation), ‘RRX’ (Rank regression on X), ‘RRY’ (Rank regression on Y). LS will perform both RRX and RRY and return the better one. 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 force_sigma - Use this to specify the sigma value if you need to force sigma to be a certain value. Used in ALT probability plotting. Optional input. kwargs are accepted for the probability plot (eg. linestyle, label, color)

Outputs: mu - the fitted Normal_2P mu parameter sigma - the fitted Normal_2P sigma 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 Normal_Distribution object with the parameters of the fitted distribution mu_SE - the standard error (sqrt(variance)) of the parameter sigma_SE - the standard error (sqrt(variance)) of the parameter Cov_mu_sigma - the covariance between the parameters mu_upper - the upper CI estimate of the parameter mu_lower - the lower CI estimate of the parameter sigma_upper - the upper CI estimate of the parameter sigma_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 LL_fs(params, T_f, T_rc, force_sigma)
static logR(t, mu, sigma)
static logf(t, mu, sigma)