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Kipchirchir, IC.  2020.  ESTIMATINGAN EXPONENTIALLY DECAYINGFUNCTION OF RATE PARAMETER OF APOISSON PROCESS. Advances and Applications in Statistics. 6(1):1-17. AbstractWebsite

In this paper, we consider point estimation of an exponentiallydecaying function of rate parameter of Poisson process usingdiscrete (increments) and continuous (interarrival times) variablesundermaximum likelihood and minimum variance paradigms. It isfound that for increments, momentsof estimators are in terms ofelementary function-the exponential function whereas for interarrivaltimes, moments of estimators are in terms of special functions-modified Bessel function ofthethirdkind for maximum likelihoodestimators and confluent hypergeometric function for the uniformlyminimum variance unbiased estimators. Behaviourally, the momentsmirror the exponentially decaying function of. The maximumlikelihood estimators are biased, however, it is found thatasymptoticunbiasedness forfixedn wheren is the sample size corresponds to a

Shem Otoi Sam, Manene MM, Isaac C Kipchirchir, Pokhariyal GP.  2020.  Cointegration analysis of youth unemployment in Kenya. International Journal of Statistics and Applied Mathematics. 5(3):129-133. AbstractWebsite

In this paper analysis of contribution of macroeconomic variables gross domestic product (GDP), external debt (ED), foreign direct investment (FDI), private investment (PI), youth population (POP), and youth literacy rate (LR) to youth unemployment(YUN) in Kenya over time is done. The analysis is done under framework of cointegration of time series data. First, logarithmic transformation of the series is carried out followed by stationarity test to determine the order of stationarity. The Philip-Ouliaris cointegration test is carried out to determine whether the series are individually cointegrated in a pair-wise manner. Then the Johansen cointegration test is conducted to determine the rank of cointegration. The paper does not proceed to identify cointegration relations as that is superfluous as far as estimation of linear cointegration model is concerned. Finally the linear cointegration equation of the macroeconomic variables is estimated and interpreted. Philip-Ouliaris test reveals that six pairs are I(0) while 15 pairs are I(1). The Augmented Dickey-Fuller test finds that GDP, FDI, and ED are stationary at level, i.e. without differencing whereas PI, LR, YUN, and POP are stationary of first difference. According to Johansen cointegration test, the rank of cointegration is 3, revealing three cointegration relations among the variables used. The results indicate that 1% increase in GDP, ED, FDI, and LR increases YUN by 0.356204%, 0.269%, 0.002441%, and 0.154216 respectively. Contrarily, 1% increasein population reduces youth unemployment by 0.350833%.The model is subjected to F-test and p-value test and found to be statistically significant


Kipchirchir, IC.  2019.  ON GENERALIZED DISTRIBUTIONS: THE POWER OF GENERALISING AND THE POWER SERIES CONNECTION. Far East Journal of Theoretical Statistics . 56(2):151-168. AbstractWebsite

In this paper, we consider generalised distributions in the context of modelling dispersion but with focus on probability generating function (pgf) which is an important tool in studying statistical properties of a discrete distribution. The aim of this paper is twofold, one is to demonstrate the power of generalising in determination of pgf and two is to show that relationship between power series can naturally lead to pgf of a generalised distribution. Generalised Poisson distributions such as negative binomial, Pólya-Aeppli and Neyman type A are used to model overdispersed (clustered) populations and they all have Poisson as a limiting distribution as contagion breaks down to randomness. In particular, the Pólya-Aeppli distribution served as a typical example in underpinning the inherent power of generalising in determining the pgf. Based on the power series distributions, it is affirmed that negative binomial distribution is a generalised Poisson distribution by utilising the relationship between exponential,

Shem Otoi Sam, Pokhariyal GP, hir Moses M Manene, Kipchirc IC.  2019.  Autoregressive distributed lag cointegration analysis of youth unemployment in Kenya. International Journal of Statistics and Applied Mathematics. 4(1):29-41. AbstractWebsite

In this paper we consider cointegration analysis in an autoregressive distributed lag (ARDL) structure. First, logarithmic transformation is performed on the series to reduce outlier effects and have elasticity interpreted in terms of percentage. Second, the variables are tested for stationarity using Augmented Dickey-Fuller test. Third, the Johansen Cointegration test is carried out to examine cointegration of the series. Fourth, cointegrated dynamic ARDL model is estimated using ordinary least squares (OLS) and effects of variables and their lags interpreted. The results indicate that Gross Domestic Product (GDP) and its two-year lag are the only ones having negative effect on youth unemployment, that is, one unit increase in GDP and GDP two-year lag reduce youth unemployment by 0.207922% and 0.2052705% respectively. Also, one unit increase in External Debt (ED) and ED two-year lag reduce youth unemployment by 0.07303% and 0.009116% respectively. Furthermore, unit increase in one-year lag of youth literacy rate is the only one which reduces youth unemployment by 0.0892691%; one-year and three-year lag of population (POP) reduce youth unemployment by 0.2590455% and 4.3093119% respectively. The Foreign Direct Investment (FDI) and Private Investment (PI) do not have significant effects on youth unemployment. In the long run, increase in GDP causes increase in youth unemployment by 0.09148447%. The long run result explains that GDP growth in the country is “jobless growth” mainly in less labour intensive sectors



In this paper, dispersion, population dynamics and competition which are typical characteristic ecological properties of a population are discussed. In particular, a comparative analysis of the effect of dispersion (overdispersion and randomness) and competition (contest and scramble) on sustainability of a single species population is considered. Population sustainability by the environment is captured by the carrying capacity of the environment which is also the equilibrium of the population. In the study, the comparative analysis is restricted to positive growth of a single species population and a stable equilibrium. The results indicate that overdispersed (clustered) population contest for resources whereas random population scramble for resources. The comparative analysis established that population sustainability of overdispersed population characterized by contest competition is more than three times population sustainability of random population characterized by scramble competition.


Khadioli, N, Tonnang ZEH, Ong'amo G, Achia T, Kipchirchir IC, Kroschel J, Ru LB.  2014.  Effect of temperature on the life history parameters of noctuid lepidopteran stem borers, Busseola fusca and Sesamia calamistis. Annals of Applied Biology. 165(3):373-386.


Kipchirchir, IC.  2013.  Comparative Analysis of Dispersion Models. Advances and Applications in Statistics. 37(1):13-35.


Kipchirchir, IC.  2012.  Comparative Study of the Distributions Used To Model Dispersion. Comparative Study of the Distributions Used To Model Dispersion.


Kipchirchir, IC.  2011.  An Analysis of Sequential Sampling Strategy in Pest Control Based on Negative Binomial Distribution. ICASTOR Journal of Mathematical Sciences. 5(2):217-228.
Kipchirchir, IC.  2011.  On Ultimate Extinction Probabilities and Mean Behaviour of Spatial Patterns. Advances and Applications in Statistics. 25(1):31-45.
Kipchirchir, IC.  2011.  Modelling Dispersion using Finite Mixture of Poisson. Far East Journal of Mathematical Sciences. 56(2):161-178.
Kipchirchir, IC.  2011.  The Versatility of the Negative Binomial Distribution in Describing Dispersion. ICASTOR Journal of Mathematical Sciences. 5(1):65-78.
Kipchirchir, IC.  2011.  An Approximation of the Fisher’s Information for the Negative Binomial Parameter k. Far East Journal of Theoretical Statistics. 34(2):129-138.


Kipchirchir, IC.  2010.  The Negative Binomial Parameter k as a Measure of Dispersion. ICASTOR Journal of Mathematical Sciences. 4(2):197-207.



Kipchirchir, IC.  1993.  An Age Structured Population Model. , Nairobi: Nairobi

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