Let {Xi, i ≥ 1} denote a sequence of {0, 1}-variables and suppose that the sequence forms a Markov Chain. In the paper we study the number of successes Sn = X1 + X2 + · · · + Xn and we study the number of experiments Y (r) up to the r-th success. In the i.i.d. case Sn has a binomial distribution and Y (r) has a negative binomial distribution and the asymptotic behaviour is well known. In the mo...

the seasonal abundance patterns of the cotton aphid, aphis gossypii glover, in cotton fields at gorgan in northern iran were studied during two growing seasons of 2002 and 2003. the spatial distribution of different developmental stages and morphs of the aphid was described by fitting data to poisson (random) and negative binomial (aggregated) dis-tributions, and calculating the dispersion indi...

Motivated by the study of cyclic resultants, we consider the problem of determining when two binomial factorizations of the form

Penna (2011) asks whether subjects with different follow-up times can be analysed through binomial regression. The answer to this question is “yes”. If the rate for a particular person is λ and they have been observed for a period of time (t), then the probability (p) of having an event during that time is equal to 1-e-λt. The equation can be re-arranged to give log[log(1-p)] = log(λ)+log(t). T...

A main application for mRNA sequencing (mRNAseq) is determining lists of differentially-expressed genes (DEGs) between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softw...

Despite remarkable gains in life expectancy and declining mortality in the 21st century, in many places mostly in developing countries, adult mortality has increased in part due to HIV/AIDS or continued abject poverty levels. Moreover many factors including behavioural, socio-economic and demographic variables work simultaneously to impact on risk of mortality. Understanding risk factors of adu...