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Journal of Biostatistics and Epidemiology، جلد ۲، شماره ۳، صفحات ۱۳۰-۱۳۵
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| چکیده فارسی مقاله |
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| کلیدواژه‌های فارسی مقاله |
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| عنوان انگلیسی |
A generalization of the negative binomial distribution |
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| چکیده انگلیسی مقاله |
Background & Aim: Consider a sequence of independent Bernoulli trials with p denoting the probability of success at each trial. With this definition, the probability that the nth success proceed by r failures follows the negative binomial distribution (NB). NB model has been derived from two different forms. At first, the NB can be thought as a Poisson-gamma mixture. The second form of the NB can be derived as a full member of a single parameter exponential family distribution, and therefore considered as a GLM (generalized linear models). Methods & Materials: We have described a new generalized NB (GNB) distribution with three parameters α, β and k obtained as a compound form of the generalized Poisson and gamma distributions. This distribution gives a very close fit for a large number of data and provides an appropriate model for numerous studies. The most important feature of this model is, its time dependent probabilities, and also it can be used for a variety of researches especially in the survival analysis. Results: This model has been illustrated with two datasets that are indirect measures of illness, along comparing the results of the fitting with NB. Results indicate too much satisfaction. Expected frequencies have been calculated for these data sets to show that the distribution provides a very satisfactory fit in different situations. Conclusion: Using GNB models allows analyzing very complex data. This distribution gives a very close fit for a large number of data and provides an appropriate model for numerous studies. With k = 0 the model becomes the ordinary NB and with α = 1, it becomes a new model which we call it the generalized geometric distribution with two parameters. The most important feature of this model is its time-dependent probabilities. |
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| کلیدواژه‌های انگلیسی مقاله |
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| نویسندگان مقاله |
مریم ناظمی پور | maryam nazemipour
department of epidemiology and biostatistics, school of public health, international campus, tehran university of medical sciences, tehran, iran
سازمان اصلی تایید شده: دانشگاه علوم پزشکی تهران (Tehran university of medical sciences)
محمود محمودی | mahmood mahmoudi
department of epidemiology and biostatistics, school of public health, tehran university of medical sciences, tehran, iran
سازمان اصلی تایید شده: دانشگاه علوم پزشکی تهران (Tehran university of medical sciences)
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| نشانی اینترنتی |
http://jbe.tums.ac.ir/index.php/jbe/article/view/110 |
| فایل مقاله |
اشکال در دسترسی به فایل - ./files/site1/rds_journals/362/article-362-420986.pdf |
| کد مقاله (doi) |
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| زبان مقاله منتشر شده |
en |
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| نوع مقاله منتشر شده |
Original Article(s) |
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