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If data values are sorted from smallest to largest, they produce a sequence of monotonically increasing data. Statistics with random variables ordered from smallest to largest value are called order statistics. The ordered statistics will be applied to exponentially distributed data. The exponential distribution is the distribution of random variables that spread according to the exponential function. The statistical method discussed is probability density function of exponential distribution of order statistics. This function is useful for creating cumulative distribution and reliability functions from ordered statistic. Random variables that are processed, namely minimum, median, and maximum of random variables. The probability density function is useful for determining the probability distribution of a random variable. The cumulative distribution function is useful for knowing the maximum value of a random variable. Meanwhile the reliability function is useful for knowing the minimum value of a random variable. They will process all ordered statistics random variables from the smallest value to the largest value. These functions will be applied at lamp lifetime. This study be assumed that lamp lifetime is exponentially distributed. The problem in this research is how to determine minimum, median, and maximum values of lamp life. While the aim of this study is to construct a probability density function from exponential distribution of order statistics, in order to obtain minimum, median, and maximum lamp lifetime. The lamp lifetime will be predicted using cumulative distribution and reliability functions. Based on calculation obtained the result that minimum value of ordered statistics that lamp lifetime is 3.5 months, median value of ordered statistics that lamp lifetime is 220 months, and maximum value of ordered statistics that lamp lifetime is 240 months. By knowing lifetime of lamp by reliability, the company can determine length of warranty period for the lamp product. [ABSTRACT FROM AUTHOR]

The classical method is a statistical method with computations according to a general formula. While the Bayes method is a method for finding statistical values based on prior distribution, likelihood function, and posterior distribution. There are data with normal distribution from the result of data generation. Statistical values of normally distributed data were determined using the classical method and the Bayes method. This research wants to know the advantages of the Bayes method over the classical method based on statistical values consisting of mean, variance, precision distribution, and confidence interval. The result of this research be obtained that the variance of posterior distribution is less than the variance of normal distribution, the Bayes method is better for data with large sample size, the precision value of the Bayes method is greater than the classical method, the length of confidence interval the Bayes method is shorter than the classical method for the same mean, and result of decision of hypothesis test between two methods is the same, too. A superior method will produce high prediction accuracy, so that resulting information has a minimal bias value. [ABSTRACT FROM AUTHOR]

Financial companies use credit scoring models to evaluate the potential borrower in advance of the insolvency risk caused by credits that enter into default. In this paper, we focus on formulating the probability of default using survival analysis with accelerated failure time, which regresses the logarithm of the survival time over the covariates, which has seldom been utilized in the study of censored survival data. Hence, we proposed this method based on the key idea of predicting the time customer will default. This paper aims to use a parametric model specifically an Exponential AFT model which is the simplest yet a good model to use when the other models are better but much complex. After we found the model, we compared the actual result with the predicting result using Mean Absolute Percentage Error (MAPE). As a result, it concludes that 98.15% of the Exponential AFT model is suitable to determine the specific factors and local factors that play an essential role in predicting the credit score of potential borrowers to determine the duration of a loan. [ABSTRACT FROM AUTHOR]

Survival analysis provides us with tools to model the time of death or failure of organisms. The concept of survival analysis can be successfully used in many different situations. This paper presents parametric survival analysis models, particularly the accelerated failure time model with Weibull distributed survival time. Next, we investigate the application of this model in analyzing credit scoring using client credit data, such as credit payment status, loan amount, interest and loan type, and client background. Credit scoring is a tool to predict the financial risk of loan clients and assist banks in analyzing new loans to be given to clients, which helps strengthen the credit risk management system. This methodology is applied to a personal loan dataset provided by credit bank in Indonesia. Accelerated Failure Time (AFT) is an alternative to parametric survival. The explanatory variable acts as an acceleration factor to accelerate or slow down the survival process compared to the baseline survival function. Consequently, it was found that the AFT model measures the direct effect of the explanatory variable on survival time, not hazard. The model meets the criteria of suitable or ideal so that the results can select clients who will receive credit. The Mean Absolute Percentage Error (MAPE) criterion compares the actual results with the predicted results to obtain the best model. This method also analyzes the factors that contribute to AFT using information from clients' credit applications as well as information provided in their credit reports. The prediction results are then assessed for accuracy with MAPE is 18.035%, this value means 81.965% of the model's good criteria to predict the client's default time. [ABSTRACT FROM AUTHOR]