Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
A Zero-truncated Discrete Quasi Lindley Distribution with Applications
Uygulamalarla Sıfır Kesikli Yarı Lindley Dağıtımı
Rama SHANKERa, Kamlesh Kumar SHUKLAb
aDepartment of Statistics, Assam University, Silchar, Assam, INDIA bDepartment of Statistics, College of Science, EIT, Asmara, ERITREA
Turkiye Klinikleri J Biostat. 2021;13(1):1-12
doi: 10.5336/biostatic.2020-76457
Article Language: EN
Full Text
ABSTRACT
 Objective: Zero-truncated distributions are used to model count data when the data originate from a mechanism excluding zero counts. Zero excluding data can be generated if the recording mechanism is not activated unless at least one event occurs. There are many real life situations where the frequency of zero-counts cannot be observed in the random experiment. For example, if a survey is related to the number of household having at least one boy child, then the frequency of zero boy children is not possible. Objective of this research is to propose a zero-truncated discrete quasi Lindley distribution and study its behavior and properties both theoretically and graphically. Material and Methods: The definition of zerotruncation has been used to derive the zero-truncated discrete quasi Lindley distribution. All the properties of the proposed discrete distribution have been derived. Results: The generating functions, moments about origin and moments about the mean of zero-truncated discrete quasi Lindley distribution have been obtained. Natures of coefficient of variation, skewness, kurtosis, and the index of dispersion of the distribution have been explained. Maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Conclusion: Applications of the distribution have been explained through four examples of observed real datasets from biological sciences and demography and its goodness of fit has been found quite satisfactory over zero-truncated Poisson-Lindley distribution, zero-truncated discrete Lindley distribution and zero-truncated quasi Poisson-Lindley distribution.

Keywords: Zero-truncated distribution; discrete Lindley distribution; moments based measures; estimation; applications
ÖZET
 Amaç: Veriler sıfır sayımlarını dışlayan bir mekanizmadan kaynaklandığında sıfır kesikli dağılımlar kullanılır. En az bir olay meydana gelmedikçe kayıt mekanizması etkinleştirilmezse sıfır dışlama verileri üretilebilir. Rastgele deneyde sıfır sayım sıklığının gözlemlenemediği birçok gerçek yaşam durumu vardır. Örneğin, bir anket en az bir erkek çocuğu olan hane halkı sayısıyla ilgiliyse, sıfır erkek çocuk sıklığı mümkün değildir. Bu araştırmanın amacı, sıfır kesikli bir Lindley dağılımını önermek ve davranışını ve özelliklerini hem teorik hem de grafiksel olarak incelemektir. Gereç ve Yöntemler: Sıfır kesikli yarı Lindley dağılımı elde etmek için sıfır kesikli tanımı kullanılmıştır. Önerile kesikli dağılımın tüm özellikleri elde edilmiştir. Bulgular ve Sonuç: Üreten fonksiyonlar, başlangıç ile ilgili momentler ve sıfır kesikli yarı Lindley dağılımının ortalaması ile ilgili momentler elde edilmiştir. Dağılımın değişkenlik katsayısı, çarpıklığı, basıklığı ve dağılım indeksi açıklanmıştır. Dağılım parametrelerini tahmin etmek için maksimum olasılık tahmini tartışılmıştır. Sonuç: Dağılım uygulamaları dört biyolojik bilimlerden gözlemlenen gerçek veri kümelerinin örnekleri ve demografi ve uyum iyiliği, sıfır kesikli Poisson-Lindley dağılımı, sıfır kesikli ayrık Lindley dağılımı ve sıfır kesilmiş yarı Poisson Lindley dağılımına göre oldukça tatmin edici bulunmuştur.

Anahtar Kelimeler: Sıfır kesikli dağılım; ayrık Lindley dağılımı; momente dayalı ölçümler; tahmin; uygulamalar
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