رسائل دكتوراة
English
2022
ON TRUNCATED DISTRIBUTIONS
كريمة عبد الكاظم مخرب, كوثر فوزي حمزة عباس
كلية التربية للعلوم الصرفة-جامعة بابل · العراق
It is complex and difficult to model natural phenomena easily. For this reason, statistical distributions are considered very significant in describing these phenomena experienced by researchers. In this study, we concentrated on truncated distributions that have multiple truncations since they are suitable for representing natural phenomena that cannot be studied or tracked in all their growth and development stages. For example, phenomena related to agriculture, airplanes, health, and the environment.
This study introduces multi-truncated distributions depending on double and left truncation. We constructed the formula to find multi-truncated continuous distributions with double truncation type and obtained their statistical properties. Multi-double truncated Weibull distribution and multi-double truncated Rayleigh distribution have been employed. Some examples of multi-double truncated distributions, such as one double-truncated Weibull distribution, one double-truncated Rayleigh distribution, and two double-truncated Weibull distributions, have been introduced, in addition to the statistical properties for each one.
Besides, we utilized the left truncation to introduce a formula that describes multi-truncation of the left truncated distributions with their statistical properties. We explained this construction through two examples, with three subintervals being cutoff. The triple-truncated Rayleigh distribution and the triple-truncated exponential distribution are presented, along with the rth moment about the origin and mean, the moment generating and characteristic functions, and order statistics. Further, all the above distributions are presented graphically.
We used the maximum likelihood method to estimate the parameters of the distributions. Also, the performance of each distribution was tested by calculating some statistical criteria (AIC, CAIC, BIC, and HQIC) and testing the goodness of fit for each distribution, with comparisons between the distributions and testing them on real data for patients infected with COVID-19 in Babylon city.