There is a problem arising when Lindley distribution is used to model right-skewed and unimodal data, which lies in its inability to model data with its peak farther from 0. A modification is required to increase the flexibility of this distribution, with “transformed-transformer” being one of the proposed method. This method is done by making a composition of two random variables through their respective distribution functions, with random variable T being the”transformed”, and random variable X being the”transformer”. In this paper, Lindley distribution was chosen to be the”transformed” and exponential distribution was chosen to be the”transformer”, constructing the Lindley-exponential distribution. However, there is a trouble using distribution if the data has a heavier tail. An alternative distribution is required while maintaining the properties of the Lindley-Exponential Distribution. Through transformation of variables method, a new distribution, Lindley-Exponential Slash Distribution is introduced, which is unimodal, right-skewed, heavier tailed. This paper covered some of its statistical characteristics, such as pdf, cdf, survival function, hazard rate, kth moment, mean, variance, skewness, and kurtosis. Parameter estimation was carried out with maximum likelihood estimation through numerical method. An application of distribution was illustrated on maximum annual precipitation data of Durham City.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 12 Jan 2021|
|Event||2nd Basic and Applied Sciences Interdisciplinary Conference 2018, BASIC 2018 - Depok, Indonesia|
Duration: 3 Aug 2018 → 4 Aug 2018
- Maximum likelihood estimation
- Slash distribution
- Transformation of variables