Mathematics and Statistics

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    Mathematical model for Tanzania population growth
    (Tanzania Journal of Science, 2019) Mwakisisile, Andongwisye; Mushi, Allen R.
    In this paper, a mathematical model for Tanzania population growth is presented. The model is developed by using exponential and logistic population growth models. Real data from censuses conducted by Tanzania National Bureau of Statistics (NBS) are used. The Tanzania growth rate is obtained by using data of 1967 and 2012 censuses. The prediction of population for the period of 2013 to 2035 is done. Numerical results show that the population grows at the rate of 2.88%. In 2035 the population is expected to be 87,538,767 by exponential model and 85,102,504 by logistic model. The carrying capacity is 2,976,857,550, which implies that the population will still grow faster since it is far from its limiting value. Comparisons of the models with real data from the five censuses are done. Also NBS projections are compared with populations predicted by the two models. Both comparisons show that the exponential model is performing better than logistic model. Also, the projection up to 2050 gives the population of 135,244,161 by exponential model and 131,261,794 by logistic model.
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    Probabilistic weather forecasting using Bayesian Model averaging: the case of Sagcot Regions
    (Mzumbe University, 2018) Joel, Emmanuel
    Over the past decade Tanzania has experienced spontaneous population increase (1.556 mil annual). But the number is estimated to further increase by 2050 to 2.982 mil annual, thus Tanzania is estimated to have population of 137 million people in 2050 (UN, 2015). The fast growing population is mainly depending on rainfed agriculture, which contribute 29 percent of the country GDP and providing employment to 65.5 percent of Tanzanians (Deloitte, 2016). The diversity in climatic and weather activities has posed a challenge in rainfed agriculture especially on when to plant seeds. Therefore, in order to promote agricultural activities, stable and reliable weather information are crucial in order for production to match with population increase. This study explores the challenge facing the Numerical Weather Prediction (NWP) namely WRF-ARW, by creating the system of equation (ensembles) from WRF-ARW resulting from the use of different initial conditions. Ensemble allow for probabilistic forecast to take the form of predictive probability function (PDF). But, raw ensemble forecast system are finite hence they only capture some of the uncertainty of the NWP. Thus, this study used Bayesian Model Averaging (BMA) methods of post processing ensemble forecast to maximize the sharpness of the parameter and calibration. The findings show BMA method successively removes most of under disersion showed by raw ensembles. Thus, calibrated and sharp results of BMA approach resolves a number of the weaknesses of the ensemble forecasts including their under dispersion and the discrepancy between forecasts and observations. Therefore, BMA can be used to attain higher consistency in the probabilistic forecasts of an operational model.