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Fit_Exponential_2P

class reliability.Fitters.Fit_Exponential_2P(failures=None, right_censored=None, show_probability_plot=True, print_results=True, CI=0.95, percentiles=None, method='MLE', optimizer=None, **kwargs)

Fits a 2-parameter Exponential distribution (Lambda,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. 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 kwargs are accepted for the probability plot (eg. linestyle, label, color)

Outputs: Lambda - the fitted Exponential_2P lambda parameter Lambda_inv - the inverse of the Lambda parameter (1/Lambda) gamma - the fitted Exponential_2P 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 - an Exponential_Distribution object with the parameters of the fitted distribution Lambda_SE - the standard error (sqrt(variance)) of the parameter Lambda_SE_inv - the standard error of the Lambda_inv parameter gamma_SE - the standard error (sqrt(variance)) of the parameter. This will always be 0. Lambda_upper - the upper CI estimate of the parameter Lambda_lower - the lower CI estimate of the parameter Lambda_upper_inv - the upper CI estimate of the Lambda_inv parameter Lambda_lower_inv - the lower CI estimate of the Lambda_inv 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 the 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)

*Note that this is a 2 parameter distribution but Lambda_inv is also provided as some programs (such as Minitab and scipy.stats) use this instead of Lambda

static LL(params, T_f, T_rc)
static LL_inv(params, T_f, T_rc)
static logR(t, L, g)
static logf(t, L, g)