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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% increase in population reduces youth
unemployment by 0.350833%.The model is subjected to F-test and p-value test and found to
be statistically significant.


S Mbala, Manene MM, Ottieno JAM.  2019.  Symmetric truth detection model: A randomized response approach. International Journal of Statistics and Applied Mathematics. 4(4):50-55. AbstractWebsite

When collecting sensitive information on abortion, drug addiction, examination dishonesty and tax
evasion among others, many researchers use direct questioning which may not yield valid data. This is
because respondents fear embarrassment and victimization. In this study we have formulated a
Symmetric Truth Detection Model which uses two randomization devises to protect the privacy of
respondents leading to a more honest response. This model is more efficient than the earlier models
namely the Asymmetric Truth detection Models

Shem Otoi Sam, Pokhariyal GP, Manene MM, Kipchumba IC.  2019.  Reparameterization of vector error correction model from auto-regressive distributed lag to analyze the effects of macroeconomic shocks on youth employment in Kenya. International Journal of Statistics and Applied Mathematics. 4(1)::05-17. AbstractWebsite

This study analyzes the effects of reparameterization of autoregressive distributed lag (ARDL) to vector error correction model (VECM) through cointegration of time series. It further verifies the effects of macroeconomic shocks on youth unemployment in Kenya using VECM. First, the unit root test has been done on youth unemployment (YUN), gross domestic product (GDP), external debt (ED), foreign direct investment (FDI), private investment (PI), youth literacy level (LR), and youth population (POP) to verify stationarity. The Johansen Cointegration Test has been employed and revealed three long run relationships which can be interpreted as a GDP effect, External Debt effect and Foreign Direct Investment effect relations. A structural VECM has been described through restrictions derived from the Cointegration Analysis. Based on the results of the Impulse-Response Function analysis and variance decomposition analysis of the Structural VECM, it is concluded that GDP, literacy level, population, Private Investment, External and FDI shocks have significant effects on Kenyan youth unemployment in the long run. Based on the results of the Impulse-Response Function and variance decomposition analyses of the Structural VECM, it is concluded that GDP, literacy level, population, and FDI shocks have significant effects on Kenyan youth unemployment in the long run. Whereas population, external debt, private investment, and GDP have positive effects, foreign direct investment and literacy rate have negative effects on youth unemployment in the long run. The results provide a statistical basis for assessing and prioritising investment policies and …

Shem Otoi Sam, Pokhariyal GP, Manene MM, Isaac C Kipchirchir.  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.


Muthama, NJ, M Moses Manene, Ndetei CJ.  2017.  Simulation of decadal precipitation over Nairobi in Kenya. Journal For Science. 13:43-54. AbstractWebsite

: In investigating Kenya rainfall variability and its relationship to other climatic
elements it has become imperative to analyze the irregularly distributed rainfall events in time.
To meet this requirement, this study used a stepwise regression technique. The study seeks to
improve existing rainfall monitoring and prediction in Nairobi. Monthly rainfall data was fitted
to several mathematical functions. The best mathematical model which best simulated the
March-May (MAM) and October -December (OND) seasonal rainfall over the three stations of
analysis was chosen using a stepwise regression technique. The value of R-squared for the best
fit was computed to show the percentage of rainfall information that is explained by the
variation in the independent (time) variable. From the results obtained, the stepwise regression
technique selected the fourth degree polynomial as the best fit for analyzing the March-May
(MAM) and October -December (OND) seasonal rainfall data set. Solar cycle period of ten (10)
years was employed to get the fourth degree polynomial variables. Hence from the study, it can
be deducted that the 4th degree polynomial function can be used to predict the peak and the
general pattern of seasonal rainfall over Nairobi, with acceptable error values. This information

Kevin John Oratungye, Oludhe C, Moses Mwangi Manene, Komutunga E.  2017.  A multivariate analysis approach in determining potential hotspots of seasonal rainfall change over Uganda. International Journal of Statistics and Applied Mathematics. 2(1):31-41. AbstractWebsite

Evidence of climate change continues to emerge in Uganda as indicated by recent floods in Teso subregion and Kasese district, landslides in Bududa and long droughts experienced in Karamoja. The major objective of the study was to identify potential hotspots of rainfall change in Uganda during March-May and October-December seasons. Monthly rainfall data for the period extending from 1951 to 2010 were used in the study. ArcGIS, a geographic information system tool was used to determine geographical areas that have experienced changes in seasonal rainfall over the decades 1981-2010 relative to the longterm mean (1951-2010). Mbale, Mbarara and Moroto were identified as areas of potential rainfall change. The historical rainfall series for the identified areas were tested for inhomogeneities using Standard Normal Homogeneity and Pettitt tests and found to be homogenous. Multivariate two-sample Hotelling T2-test was used to generate evidence of rainfall change in the identified areas by comparing mean seasonal rainfall vectors between the sub-periods 1951-1980 and 1981-2010. Results indicated a significant simultaneous decrease in mean rainfall over Moroto and Mbarara areas across the March-May season with April having the highest decrease (11 mm and 18 mm respectively). Mean rainfall in Mbale was found to have increased simultaneously across both wet seasons with April and October experiencing the greatest increase (10 mm apiece). These changes have detrimental effects on crop and livestock farming as well as human lives. There is need for increased climate change adaptation and resilience action in the …


DAVIS NTWIGA, Weke P, Manene M, Mwaniki J.  2016.  International Journal of Mathematical Archive-7 (2), 2016, 64-68 Available online through www. ijma. info ISSN 2229–5046. International Journal of Mathematical Archive. 7(2):,64-68. AbstractWebsite

We rely on trust in our day to day interactions and activities with each other. It is not easy to estimate it but we offer a simple and powerful method for estimating trust levels of agents in a social network using data from the agents’ reputation matrix. The reputation resultant method (RRM) is based on the mean values of the reputation rating matrix and the reputation resultant matrix. Reputation ratings are derived from the agents’ peer to peer ratings and the resultant reputation data is the relative reputation ratings by the agents. A comparison is made between the results of Singular value decomposition (SVD) and our new method, the RRM. The two methods offer results that are highly comparative with the RRM being simple, powerful and easy to understand and implement.


Keroboto BZ Ogutu, Fabio D'Andrea, Michael Ghil, Nyandwi C, Manene MM, Mutha JN.  2015.  Coupled Climate–Economy–Biosphere (CoCEB) model–Part 2: Deforestation control and investment in carbon capture and storage technologies. Earth System Dynamics Discussions. 6(1):865-906. AbstractWebsite

This study uses the global climate–economy–biosphere (CoCEB) model developed in Part 1 to investigate economic aspects of deforestation control and carbon sequestration in forests, as well as the efficiency of carbon capture and storage (CCS) technologies as policy measures for climate change mitigation. We assume – as in Part 1 – that replacement of one technology with another occurs in terms of a logistic law, so that the same law also governs the dynamics of reduction in carbon dioxide emission using CCS technologies. In order to take into account the effect of deforestation control, a slightly more complex description of the carbon cycle than in Part 1 is needed. Consequently, we add a biomass equation into the CoCEB model and analyze the ensuing feedbacks and their effects on per capita gross domestic product (GDP) growth. Integrating biomass into the CoCEB and applying deforestation control as well as CCS technologies has the following results: (i) low investment in CCS contributes to reducing industrial carbon emissions and to increasing GDP, but further investment leads to a smaller reduction in emissions, as well as in the incremental GDP growth; and (ii) enhanced deforestation control contributes to a reduction in both deforestation emissions and in atmospheric carbon dioxide concentration, thus reducing the impacts of climate change and contributing to a slight appreciation of GDP growth. This effect is however very small compared to that of low-carbon technologies or CCS. We also find that the result in (i) is very sensitive to the formulation of CCS costs, while to the contrary, the results for deforestation control are less …


Manene, MM, Muthama NJ, Ndetei CJ.  2013.  Use Of Polynomial Fit To Predict Seasonal Rainfall In Nairobi, Kenya.





Manene, MM, Odhiambo JW.  1987.  Probability and Statistics I.
Odhiambo, J. W. and Manene, MM.  1987.  Step-wise Group Screening Designs with Errors in Observations. Commun Statist. Theor. Meth. 16(10):3095–3115.
Patel, M. S. and Manene, MM.  1987.  Step-wise Group Screening with Equal Prior Probabilities and No errors in Observations;. 16(3):817–833.

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