Confidence interval estimation of gamma distribution lifetime data using score and bootstrap methods

Confidence interval estimation of parameters determines the value interval, which is calculated based on statistical measurements and has specific estimates probability that contains the actual parameters. A method is needed to estimate the parameters' confidence interval, and the methods used are the Score method and the Bootstrap method. This study aims to estimate parameters by using the maximum likelihood estimation method and analyze the reliability of the aircraft engine cooling system's lifetime that follows the Gamma Distribution, and estimate the confidence interval of the parameters

The Annual Premium of Life Insurance on The Joint-Life Status based on The 2011 Indonesian Mortality Table

Life insurance is insurance that protects against risks to someone's life. Joint Life Insurance is insurance where the life and death rules are a combination of two or more factors, such as husband-wife or parent-child, and if the first death occurs, then the premium payment process is stopped. The annual premium is the premium paid annually. In this study, the annual premium is calculated continuously with the equivalence principle based on the 2011 Indonesian Mortality Table.  The calculation shows that the amount of annual premiums for 2 (two) and 3 (three) people is not much different. The factors that influence the annual premium amount are the duration insurance period, age at signing the policy, interest rates, life chances, force of mortality, and the number of benefits

Asosiasi Keterjadian Koloni Verticillium Dan Intensitas Naungan Serta Letak Daun Kopi

Association of Verticillium colony intensity and shade and coffee leaf position. Since conventional control methods of leaf rust of coffee is still unsatisfactory, it is needed to study toward the possibility of using biocontrol agents including factors that may influence the occurrence of the agents. The objective of this study was to determine the strength of the association of Verticillium colony occurrence and shade and leaf position. Leaf samples were taken from four sites at three coffee fields at Sumberjaya Sub district, West Lampung. Samples were taken from plants with and without shade. From each shade level, leaves showing symptoms were taken from the plants and from the ground (fallen leaves). The samples were placed individually on plastic bag and transported to the laboratory, where the samples were incubated for four days at room temperature. The proportion of lesion caused by H. vastatrix on coffee leaves that showed whitish Verticillium colonies was recorded and modified to score 0 (without Verticillium colony) to 4 (colony 50% or more). Data were analyzed with log linear saturated model. Data suggested that the occurrence of Verticillium colony was higher on plant with canopy compared to that on plants without canopy. In addition, Verticillium occurred more frequently on leaves still on the plants compared to that on leaves on the ground. Canopy factor was relatively stronger than leaf position factor in influencing the occurrence of Verticillium colony

Simulasi Jumlah Klaim Agregasi Berdistribusi Poisson Dengan Besar Klaim Berdistribusi Gamma dan Rayleigh

A claim is a transfer of risk from the insured to the guarantor. Claims that occur individually are called individual claims, whereas collections of individual claims are called aggregation claims in a single period of vehicle insurance. Aggregation claims consist of a pattern of the number and amount (nominal value) of individual claims, so that the model of aggregation claims is formed from each distribution of the number and amount of claims. The distribution of claims is based on the probability density function and the cumulative density function. One method that can be used to obtain a claim aggregation model is to use convolution, which is by combining the distribution of the number of claims and the distribution of the amount of claims so that the expected value can be obtained to predict the value of pure premiums. In this paper, aggregation claim modeling will be carried out with the number of claims distributed Poisson and the amount of claims distributed Gamma. As comparison, we compare it with claim amount distributed Rayleigh. By using VaR (value at risk) and MSE (Mean Square Error) indicators, the results of the analysis show that the Rayleigh distribution is better used for distributing data that has extreme values

Simulasi Jumlah Klaim Agregasi Berdistribusi Poisson dengan Besar Klaim Berdistribusi Gamma dan Rayleigh

A claim is a transfer of risk from the insured to the guarantor. Claims that occur individually are called individual claims, whereas collections of individual claims are called aggregation claims in a single period of vehicle insurance. Aggregation claims consist of a pattern of the number and amount (nominal value) of individual claims, so that the model of aggregation claims is formed from each distribution of the number and amount of claims. The distribution of claims is based on the probability density function and the cumulative density function. One method that can be used to obtain a claim aggregation model is to use convolution, which is by combining the distribution of the number of claims and the distribution of the amount of claims so that the expected value can be obtained to predict the value of pure premiums. In this paper, aggregation claim modeling will be carried out with the number of claims distributed Poisson and the amount of claims distributed Gamma. As comparison, we compare it with claim amount distributed Rayleigh. By using VaR (value at risk) and MSE (Mean Square Error) indicators, the results of the analysis show that the Rayleigh distribution is better used for distributing data that has extreme values

Higher dimensional log-linear model and its application

: In this study the model of higher dimensional log-linear model is applied to four categorical variables in Education. The data are collected from the alumni data of University of Lampung, from 2010 to 2013 and about 9060 alumni involved. In this study, the variables of interest are: Length of Study with three categories (5.5 years), Field of Study with three categories (Sciences, Social Sciences, and Education), Sex with two categories (Male, and Female), GPA in scale 0 to 4 with three categories ( 3.5). In this study the aims are going to find the best model to explain the relationship among the factors. By using hierarchical Log-linear Model Analysis and backward method it was found that the best model for the data with three variables interactions in the model are: Length of Study*SEX*GPA, Length of Study*Sciences*GPA, and Sex*Sciences*GPA

Comparison of some methods of testing hypothesis in unbalanced split plot design

Missing observations in split plot design create many analysis problems. In this article, we consider the testing hypotheses problems for a split plot design with missing subplots and whole plots. Some methods of testing hypotheses in unbalance split plot design are presented and the performances of the methods are compared based on the type I error and its power of the test. Simulation studies were conducted to compare the performance of various method