How to use the reliability.Distributions.Exponential_Distribution function in reliability

if max(X) <= 1:  # condition for Beta Dist to be fitted
            Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta).PDF(xvals=xvals, label=r'Beta ($\alpha , \beta$)')
        plt.legend()
        plt.xlim([xmin, xmax])
        plt.title('Probability Density Function')
        plt.xlabel('Data')
        plt.ylabel('Probability density')
        plt.legend()

        plt.subplot(122)  # CDF
        plt.bar(center, hist_cumulative * self._frac_fail, align='center', width=width, alpha=0.2, color='k', edgecolor='k')
        Weibull_Distribution(alpha=self.Weibull_2P_alpha, beta=self.Weibull_2P_beta).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta$)')
        Weibull_Distribution(alpha=self.Weibull_3P_alpha, beta=self.Weibull_3P_beta, gamma=self.Weibull_3P_gamma).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta , \gamma$)')
        Gamma_Distribution(alpha=self.Gamma_2P_alpha, beta=self.Gamma_2P_beta).CDF(xvals=xvals, label=r'Gamma ($\alpha , \beta$)')
        Gamma_Distribution(alpha=self.Gamma_3P_alpha, beta=self.Gamma_3P_beta, gamma=self.Gamma_3P_gamma).CDF(xvals=xvals, label=r'Gamma ($\alpha , \beta , \gamma$)')
        Exponential_Distribution(Lambda=self.Expon_1P_lambda).CDF(xvals=xvals, label=r'Exponential ($\lambda$)')
        Exponential_Distribution(Lambda=self.Expon_2P_lambda, gamma=self.Expon_2P_gamma).CDF(xvals=xvals, label=r'Exponential ($\lambda , \gamma$)')
        Lognormal_Distribution(mu=self.Lognormal_2P_mu, sigma=self.Lognormal_2P_sigma).CDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma$)')
        Lognormal_Distribution(mu=self.Lognormal_3P_mu, sigma=self.Lognormal_3P_sigma, gamma=self.Lognormal_3P_gamma).CDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma , \gamma$)')
        Normal_Distribution(mu=self.Normal_2P_mu, sigma=self.Normal_2P_sigma).CDF(xvals=xvals, label=r'Normal ($\mu , \sigma$)')
        if max(X) <= 1:  # condition for Beta Dist to be fitted
            Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta).CDF(xvals=xvals, label=r'Beta ($\alpha , \beta$)')
        plt.legend()
        plt.xlim([xmin, xmax])
        plt.title('Cumulative Distribution Function')
        plt.xlabel('Data')
        plt.ylabel('Cumulative probability density')
        plt.suptitle('Histogram plot of each fitted distribution')
        plt.legend()

plt.subplot(121)  # PDF

        # make this histogram. Can't use plt.hist due to need to scale the heights when there's censored data
        num_bins = min(int(len(X) / 2), 30)
        hist, bins = np.histogram(X, bins=num_bins, density=True)
        hist_cumulative = np.cumsum(hist) / sum(hist)
        width = np.diff(bins)
        center = (bins[:-1] + bins[1:]) / 2
        plt.bar(center, hist * self._frac_fail, align='center', width=width, alpha=0.2, color='k', edgecolor='k')

        Weibull_Distribution(alpha=self.Weibull_2P_alpha, beta=self.Weibull_2P_beta).PDF(xvals=xvals, label=r'Weibull ($\alpha , \beta$)')
        Weibull_Distribution(alpha=self.Weibull_3P_alpha, beta=self.Weibull_3P_beta, gamma=self.Weibull_3P_gamma).PDF(xvals=xvals, label=r'Weibull ($\alpha , \beta , \gamma$)')
        Gamma_Distribution(alpha=self.Gamma_2P_alpha, beta=self.Gamma_2P_beta).PDF(xvals=xvals, label=r'Gamma ($\alpha , \beta$)')
        Gamma_Distribution(alpha=self.Gamma_3P_alpha, beta=self.Gamma_3P_beta, gamma=self.Gamma_3P_gamma).PDF(xvals=xvals, label=r'Gamma ($\alpha , \beta , \gamma$)')
        Exponential_Distribution(Lambda=self.Expon_1P_lambda).PDF(xvals=xvals, label=r'Exponential ($\lambda$)')
        Exponential_Distribution(Lambda=self.Expon_2P_lambda, gamma=self.Expon_2P_gamma).PDF(xvals=xvals, label=r'Exponential ($\lambda , \gamma$)')
        Lognormal_Distribution(mu=self.Lognormal_2P_mu, sigma=self.Lognormal_2P_sigma).PDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma$)')
        Lognormal_Distribution(mu=self.Lognormal_3P_mu, sigma=self.Lognormal_3P_sigma, gamma=self.Lognormal_3P_gamma).PDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma , \gamma$)')
        Normal_Distribution(mu=self.Normal_2P_mu, sigma=self.Normal_2P_sigma).PDF(xvals=xvals, label=r'Normal ($\mu , \sigma$)')
        if max(X) <= 1:  # condition for Beta Dist to be fitted
            Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta).PDF(xvals=xvals, label=r'Beta ($\alpha , \beta$)')
        plt.legend()
        plt.xlim([xmin, xmax])
        plt.title('Probability Density Function')
        plt.xlabel('Data')
        plt.ylabel('Probability density')
        plt.legend()

        plt.subplot(122)  # CDF
        plt.bar(center, hist_cumulative * self._frac_fail, align='center', width=width, alpha=0.2, color='k', edgecolor='k')
        Weibull_Distribution(alpha=self.Weibull_2P_alpha, beta=self.Weibull_2P_beta).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta$)')
        Weibull_Distribution(alpha=self.Weibull_3P_alpha, beta=self.Weibull_3P_beta, gamma=self.Weibull_3P_gamma).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta , \gamma$)')

if best_dist == 'Weibull_2P':
            self.best_distribution = Weibull_Distribution(alpha=self.Weibull_2P_alpha, beta=self.Weibull_2P_beta)
        elif best_dist == 'Weibull_3P':
            self.best_distribution = Weibull_Distribution(alpha=self.Weibull_3P_alpha, beta=self.Weibull_3P_beta, gamma=self.Weibull_3P_gamma)
        elif best_dist == 'Gamma_2P':
            self.best_distribution = Gamma_Distribution(alpha=self.Gamma_2P_alpha, beta=self.Gamma_2P_beta)
        elif best_dist == 'Gamma_3P':
            self.best_distribution = Gamma_Distribution(alpha=self.Gamma_3P_alpha, beta=self.Gamma_3P_beta, gamma=self.Gamma_3P_gamma)
        elif best_dist == 'Lognormal_2P':
            self.best_distribution = Lognormal_Distribution(mu=self.Lognormal_2P_mu, sigma=self.Lognormal_2P_sigma)
        elif best_dist == 'Lognormal_3P':
            self.best_distribution = Lognormal_Distribution(mu=self.Lognormal_3P_mu, sigma=self.Lognormal_3P_sigma, gamma=self.Lognormal_3P_gamma)
        elif best_dist == 'Exponential_1P':
            self.best_distribution = Exponential_Distribution(Lambda=self.Expon_1P_lambda)
        elif best_dist == 'Exponential_2P':
            self.best_distribution = Exponential_Distribution(Lambda=self.Expon_2P_lambda, gamma=self.Expon_2P_gamma)
        elif best_dist == 'Normal_2P':
            self.best_distribution = Normal_Distribution(mu=self.Normal_2P_mu, sigma=self.Normal_2P_sigma)
        elif best_dist == 'Beta_2P':
            self.best_distribution = Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta)

        # print the results
        if print_results is True:  # printing occurs by default
            pd.set_option('display.width', 200)  # prevents wrapping after default 80 characters
            pd.set_option('display.max_columns', 9)  # shows the dataframe without ... truncation
            print(self.results)

        if show_histogram_plot is True:
            Fit_Everything.histogram_plot(self)  # plotting occurs by default

        if show_PP_plot is True:
            Fit_Everything.P_P_plot(self)  # plotting occurs by default

Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta).PDF(xvals=xvals, label=r'Beta ($\alpha , \beta$)')
        plt.legend()
        plt.xlim([xmin, xmax])
        plt.title('Probability Density Function')
        plt.xlabel('Data')
        plt.ylabel('Probability density')
        plt.legend()

        plt.subplot(122)  # CDF
        plt.bar(center, hist_cumulative * self._frac_fail, align='center', width=width, alpha=0.2, color='k', edgecolor='k')
        Weibull_Distribution(alpha=self.Weibull_2P_alpha, beta=self.Weibull_2P_beta).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta$)')
        Weibull_Distribution(alpha=self.Weibull_3P_alpha, beta=self.Weibull_3P_beta, gamma=self.Weibull_3P_gamma).CDF(xvals=xvals, label=r'Weibull ($\alpha , \beta , \gamma$)')
        Gamma_Distribution(alpha=self.Gamma_2P_alpha, beta=self.Gamma_2P_beta).CDF(xvals=xvals, label=r'Gamma ($\alpha , \beta$)')
        Gamma_Distribution(alpha=self.Gamma_3P_alpha, beta=self.Gamma_3P_beta, gamma=self.Gamma_3P_gamma).CDF(xvals=xvals, label=r'Gamma ($\alpha , \beta , \gamma$)')
        Exponential_Distribution(Lambda=self.Expon_1P_lambda).CDF(xvals=xvals, label=r'Exponential ($\lambda$)')
        Exponential_Distribution(Lambda=self.Expon_2P_lambda, gamma=self.Expon_2P_gamma).CDF(xvals=xvals, label=r'Exponential ($\lambda , \gamma$)')
        Lognormal_Distribution(mu=self.Lognormal_2P_mu, sigma=self.Lognormal_2P_sigma).CDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma$)')
        Lognormal_Distribution(mu=self.Lognormal_3P_mu, sigma=self.Lognormal_3P_sigma, gamma=self.Lognormal_3P_gamma).CDF(xvals=xvals, label=r'Lognormal ($\mu , \sigma , \gamma$)')
        Normal_Distribution(mu=self.Normal_2P_mu, sigma=self.Normal_2P_sigma).CDF(xvals=xvals, label=r'Normal ($\mu , \sigma$)')
        if max(X) <= 1:  # condition for Beta Dist to be fitted
            Beta_Distribution(alpha=self.Beta_2P_alpha, beta=self.Beta_2P_beta).CDF(xvals=xvals, label=r'Beta ($\alpha , \beta$)')
        plt.legend()
        plt.xlim([xmin, xmax])
        plt.title('Cumulative Distribution Function')
        plt.xlabel('Data')
        plt.ylabel('Cumulative probability density')
        plt.suptitle('Histogram plot of each fitted distribution')
        plt.legend()

label = str('Fitted Exponential_2P\n(λ=' + str(round_to_decimals(Lambda, dec)) + ', γ=' + str(round_to_decimals(gamma, dec)) + ')')
        if 'color' in kwargs:  ####
            data_color = kwargs.get('color')  ####
        else:  ####
            data_color = 'k'  ####
        xlabel = 'Time - gamma'  ####
        failures = failures - gamma + 0.009  # this 0.009 adjustment is to avoid taking the log of 0. It causes negligible difference to the fit and plot. 0.009 is chosen to be the same as Weibull_Fit_3P adjustment.
        if right_censored is not None:
            right_censored = right_censored - gamma + 0.009  # this 0.009 adjustment is to avoid taking the log of 0. It causes negligible difference to the fit and plot. 0.009 is chosen to be the same as Weibull_Fit_3P adjustment.

        #### recalculate the xvals for the plotting range when gamma>0
        if max(failures) - gamma < 1:
            xvals = np.logspace(-5, 1, 1000)
        else:
            xvals = np.logspace(-4, np.ceil(np.log10(max(failures) - gamma)) + 1, 1000)  ####needed to adjust the lower lim here so it is > 0
    ef = Exponential_Distribution(Lambda=Lambda, Lambda_SE=Lambda_SE, CI=CI)  ####added extra params and removed .CDF

    # plot the failure points and format the scale and axes
    x, y = plotting_positions(failures=failures, right_censored=right_censored, h1=h1, h2=h2)
    plt.scatter(x, y, marker='.', linewidth=2, c=data_color)
    plt.gca().set_yscale('function', functions=(axes_transforms.weibull_forward, axes_transforms.weibull_inverse))
    plt.xscale('log')
    plt.grid(b=True, which='major', color='k', alpha=0.3, linestyle='-')
    plt.grid(b=True, which='minor', color='k', alpha=0.08, linestyle='-')
    plt.ylim([0.0001, 0.9999])
    xrange = plt.gca().get_xlim()  # this ensures the previously plotted objects are considered when setting the range
    xrange_min = min(min(x), xrange[0])
    xrange_max = max(max(x), xrange[1])
    if xrange_min <= 0:
        xrange_min = 1e-2
    pts_min_log = 10 ** (int(np.floor(np.log10(xrange_min))))  # second smallest point is rounded down to nearest power of 10
    pts_max_log = 10 ** (int(np.ceil(np.log10(xrange_max))))  # largest point is rounded up to nearest power of 10