Kondo 1 as Pearson's type X distribution when the sampling of standard deviation was discussed.These distributions have been widely used to analyze lifetime data, on account of its analytical tractability, also used in physics, queueing theory, and hydrology, often used to model the reliability of electronic systems, which do not typically experience wear-out type failures. Exponential variables can also be used to model situations where certain events occur with a constant probability per unit length, such as the distance between mutations on a DNA strand, or between road kills on a given road.
In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided.
The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.
The purpose of this study is to examine the finite sample aspects of estimates of the parameters of the weighted Lindley distribution derived by four estimation methods: maximum likelihood, method of moments, ordinary least squares, and weighted least squares, using Monte Carlo simulations. As a comparison criterion, bias and mean-squared error are used. In both small and large samples, the Cramer-von Mises approach is found to be very competing with the maximum likelihood method. To substantiate the conclusion, a statistical analysis of a real data set related to weather is performed.
This paper reviews works on Skellam distribution, its extensions and areas of applications. Available literature shows that this distribution is flexible for modelling integer data where they appear as count data or paired count data in the field of finance, medicine, sports, and science. Bivariate Skellam distribution, dynamic Skellam model and other extensions are also discussed and additional literature are provided.
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