Strathmore Institute of Mathematical Sciences (SIMs)

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The Strathmore Institute of Mathematical Sciences(SIMs) succeeds the Centre of Applied Research in Mathematical Sciences (CARMS). It is committed to delivering high quality graduate education and research through providing a stimulating research environment and continuous support for our researchers and students. SIMS promotes and develops research and consulting in the mathematical sciences, including statistics, mathematical biology, mathematical finance and mathematics education

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11-day cycle of stock prices in Kenya around profit warnings
(Strathmore University, 2020) Kagiri, Jonathan Njenga
A profit warning is a statement issued by a company in order to inform the public that the profits for a specified period will be significantly different from the expected profit levels. The Capital Markets Authority, which is responsible for the regulation of the stock exchange, in a bid to reduce the levels of information asymnetry and conflicts of interest between managers and shareholders, made it a requirement for all companies listed on the Nairobi Stock Exchange to issue profit warnings if their profit will be 25% less than what was expected. This study aims to view the abnormal returns surrounding a profit warning on the returns within a 1 0-day scope of the release of a profit warning. The theories and hypotheses this study relies on are the agency theory, the efficient market hypothesis and the signalling theory. An event study methodology was used, with abnormal returns being derived as a regression analysis result of the stock versus the market returns. The result being that the abnormal return is significantly different on the trading day after the profit warning and two days after the profit warning.
A Bayesian hierarchical model for correlation in microarray studies
Omolo, Bernard
Microarrays are miniaturised biological devices consisting of molecules (e.g. DNA or protein), called \probes", that are orderly arranged at a microscopic scale onto a solid support such as a nylon membrane or a glass slide.The array elements (probes) bind speci cally to labeled molecules, called "targets", into complex molecular mixtures,thereby generating signals that reveal the identity and the concentration of the interacting labeled cells.Microarray analysis has a broad range of applications that involve di erent types of probes and/or targets (cDNA or oligos)
A Comparative study of Hybrid Neural Network and ARIMA Models with application to forecasting intra-day child-line calls in Kenya
(Strathmore University, 2022) Wang’ombe, Grace Wairimu
Background: For successful staffing and recruiting of call centre professionals, precise forecasting of the number of calls arriving at the centre is crucial. These projections are needed for various periods, both short and long-term. Benchmark time series models such as ARIMA and Holt-Winters used in forecasting call centre data are outperformed in long term forecasts, especially when the data is not stationary. Advanced models such as the ANNs can pick up on the random peaks or outlying periods better than the benchmark time–series models. The hybrid methodology combines the strengths of the benchmark time–series and advanced models, thus improving overall forecasts. Objective: The study’s primary goal was to assess the superiority of a Hybrid ARIMAANN model over its constituent models in forecasting Childline call centre data in Kenya. Methods: The ARIMA, ANN and hybrid ARIMA-ANN models were used in the call centre data forecasting. The cross-validation technique was used to create forecasting accuracy metrics which are then compared. In ARIMA, the Box-Jenkins methodology is used to fit the model whereas the neural network element of the hybrid model and the ANN were modelled using the feed-forward Neural Network Autoregressive(NNAR) structure. Results: The Seasonal ARIMA - ANN model outperformed the ARIMA model in short term forecasts and the ANN model in long term forecasts. The Diebold-Mariano test indicated a significant difference between the hybrid and ANN forecasts, whereas the difference between the hybrid and ARIMA forecasts was not significant. Conclusion: The Hybrid model was able to adapt both of its constituent models’ advantages to better its performance. These results are helpful as call centres can be able to use one model which is robust enough to create accurate forecasts rather than the benchmark models.
A copula-based approach to differential gene expression analysis
Chaba, Linda Akoth; Odhiambo, John W.; Omolo, Bernard
Melanoma is a major public health concern in the developed world. Melanoma research has been enhanced by the introduction of microarray technology, whose main aim is to identify genes that are associated with outcomes of interest in melanoma biology and disease progression. Many statistical methods have been proposed for gene selection but so far none of them is regarded as the standard method. In addition, none of the proposed methods have applied copulas to identify genes that are associated with quantitative traits. In this study, we developed a copula-based approach to identify genes that are associated with quantitative traits in the systems biology of melanoma. To assess the statistical properties of model , we evaluated the power, the false-rejection rate and the true-rejection rate using simulated gene expression data . The model was then applied to a melanoma dataset for validation. Comparison of the copula approach with the Bayesian and other parametric approaches was performed, based on the false discovery rate (FOR) , the value of R-square and prognostic properties. It turned out that the copula model was more robust and better than the others in the selection of genes that were biologically and clinically significant.
A Mathematical model for bovine brucellosis incorporating contaminated environment
Robert, Godwin; Julius, Tumwiine
A Phase transition in the distribution of the length of integer partitions
Ralaivaosaonay, Dimbinaina
We assign a uniform probability to the set consisting of partitions of a positive integer n such that the multiplicity of each summand is less than a given number d and we study the limiting distribution of the number of summands in a random partition. It is known from a result by Erd˝os and Lehner published in 1941 that the distributions of the length in random restricted (d = 2) and random unrestricted (d n + 1) partitions behave very differently. In this paper we show that as the bound d increases we observe a phase transition in which the distribution goes from the Gaussian distribution of the restricted case to the Gumbel distribution of the unrestricted case.
A smooth test of goodness-of-fit for the baseline hazard function in recurrent event models
Odhiambo, John W.; Odhiambo, Collins; Omolo, Bernard
In this paper, we formulate a smooth test of goodness-of-fit for a simple hypothesis about the baseline hazard function in recurrent-event models. The formulation is an extension of Neyman' s goodness-of-fit approach, whose score tests are obtained by embedding the null hypothesis in a larger class of hazard rate functions. Since the application is in recurrent event models , the data is dynamic.A useful feature about this test is the parametric approach that makes inference about the hazard function more efficient. To examine the finite-sample properties of this test, we used simulated data . For validation, we applied the test to a real-life recurrent event data. Results show that the test possesses better power over wide range of alternatives, when compared with similar tests of the chi-square type in the literature.
A Systematic comparison of performance of Ridge, Lasso, Elastic net and Relaxed Elastic net when fitting high dimensional data for sales prediction
(Strathmore University, 2022) Muoki, Monica Mueni
Forecasting or prediction is one of the most crucial aspects of planning for many companies. Data-driven decisions can only be as accurate as the prediction they are based on. Some of the decisions include production planning, inventory management, and various resource allocation. Sales information is really multi-dimensional, and as a result not easy to analyse. Our motivation is to reduce the high dimension of this information, select optimal contributing variables with the aim of making accurate and reliable sales predictions. The purpose of this study is to compare the performance of four restricted regressions. This involves looking at Ridge, Lasso, Relaxed net and Elastic net regressions and assessing their performance in prediction when dealing with high dimensional data. The proposed method will involve comparison of the four mentioned regularized techniques, citing their restrictions and evaluating their prediction model performance. We will also involve data simulation to test the different models. The simulations are done under different scenarios to present the reality of a market setting. Afterwards, we will select the best model and use it to fit our real sales dataset provided by one of the leading ECMCs in Kenya. On this basis, elastic net offered best predictions based. The evaluating metrics for this models are Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and R-Squared (R2). However, the desired model based on R2 kept shifting under different scenarios to Lasso, Ridge and Elastic net. The results indicated that the regularized approaches especially elastic net are capable of dealing with non-linearity and fluctuating dynamics in manufacturing industry while predicting electrical cable sales accurately.
Adverse information on social media will always send Kenyans to withdraw their money
(2016-04) Karoney, Carol-Noelle; Kalu, Elizabeth
In the paper “The Extent to Which Social Media Can Influence a Bank Run” Atieno,T. and Mutinda, M. (2014) provided empirical evidence that there was a huge risk of a bank run occurring in Kenya due to social media. This paper co-relates that study with the closure of Chase Bank Kenya in April 2016
An Aggregate analysis of the impact factor of the index based livestock insurance pastoralists in Kenya
(Strathmore University, 2018) Matano, Del Words
The purpose of this study was to quantify the effects of Index Based Livestock Insurance in Kenya on income generation and welfare enhancement of pastoral households. Index-Based insurance attracts attention as a potentially effective tool for reducing vulnerability of agricultural household’s in developing countries. However, previous literature has assumed away how household intertemporal behavior and welfare would change by reduced production risk and shock due to index-based insurance. The paper employed the endogenous treatment regression model in order to quantify the effects of Index Based Livestock Insurance on an aggregate level. The study finds that insurance provision induces pastoralists to shift production towards higher return but higher risk breeds of livestock. The results support the view that financial innovation can mitigate the real effects of uninsured production risk.
Agricultural micro-insurance in Kenya: determinants of the loss and profit experienced in insurance companies in Kenya in 2014
(Strathmore University, 2016) Kirui, Fiona C
ABSTRACT The Kenyan agricultural production sector is faced with a lot of risks that will affect a farmer's level of income. The Kenyan insurance market offers two types of-agricultural micro insurance products, index based crop insurance and indemnity based crop insurance. This study has investigated the significant factors that affect profitability of an insurance company. To provide answers to the research questions quantitative methods were employed. Use of simulation of variables, correlation tests, and regression analysis were the major quantitative tools used to analyse the data availed. The results of the study conducted showed that companies that offer index based products are more profitable compared to companies that offer pure indemnity products. It was also noted that a combination of both products leads to a higher profit margin as opposed to offering pure based products.
An Inclusive pension model for Kenya’s informal sector with late entries and early exit rates
(Strathmore University, 2019) Lagat, Cherono Asumpta
The purpose of this study is three-fold: first, we develop 1'1 pension model that uses preretirement mobile phone airtime expenditures to accumulate the pension fund. Secondly, we · calculate the exit and entry rates into the comprehensive pension scheme. Finally, we determine the expenditure patterns experienced post-retirement and use these patterns to advise on the daily amount required to be charged per minute above the current rate in order to facilitate a comfortable post-retirement life. The data utilized in this study was retrieved from various secondary sources. Inflation and interest rates data -were retrieved from Kenya's Central Bank database. The entry and exit data into informal pension schemes was retrieved from Eagle Africa the administrators of Mbao Pension scheme the largest informal pension scheme in Kenya. The mortality rates were retrieved from the World Health Organization and the life expectancy from ·world Atlas, Lancet and World Life Expectancy. Pre-retirement data was retrieved from November 2013 from an integrated survey on land ownership and tenure, provision, access and control of basic services, asset ownership, financial resources, evictions and demolition of houses, as well as thirty-two key informant interviews with informal small-scale service provider’s facilitated by Strathmore University. The inflation and interest rates were forecasted using ARIMA (1,9,5)-GARCH (0,1) model while the backward entry and exit data points were simulated in R. Our results show that an unemployed Kenyan spends approximately KShs. 2, 000.37 a month considering inflation this amount will translate KShs. 4, 025.45 to maintain the same life style post-retirement assuming the person joins the scheme at 18 and exits at the age of 55. Given the expenditure pre-retirement of this group of people, it will require them to be charged KShs. 3.41 per minute above the current rate in order to raise an amount sufficient to sustain their lifestyle post-retirement.
Analysis of asset allocation and the financial performance of individual pension schemes in Kenya
(Strathmore University, 2015) Nzioka, Reza Matheka
Pension funds are a major source of retirement income for many people worldwide. There is an increased need to measure perfonnance of the assets held by the schemes since the growing importance of pension funds has boosted the need for methodologically sound principles for asset allocation (Swietanowski 1999). The legal owners of the scheme, the Trustees, are required to develop Investment Plans which are basically policies on the strategic asset allocation for their schemes.
An analysis of liquidity in stock markets
(Strathmore University, 2016) Muindi, Brenda Wanja
The following is a study on liquidity of the va rious stocks listed on the NSE. It has defined liquidity as the ability to trade large quantities of a stock without moving the price. The study seeks to determine the most liquid/ illiquid stocks listed on the NSE and the possible determinants of a given stock's liquidity/illiquidity. To determine the most liquid/illiquid stocks, the paper employs liquidity ratio as a measure of the stocks liquidity. The paper utilizes panel data regression and multiple regression to answer its research questions. The regressions were run using GRETL. The results suggest that Liquidity Ratio is an appropriate measure of liquidity in the NSE. The results also suggest that companies with high presence on social media as well as a high number of issued stocks tend to be more liquid. Keywords: Liquidity, Nairobi Securities Exchange
An analysis of longevity risk in a portfolio of life annuitants
(Strathmore University, 2015) Njeri, Sharon
Longevity risk has economic significance for governments, individuals and corporations. There is need to analyze the expected future lifetime of a population anticipating to receive lifetime benefits in Kenya. This paper performs such an analysis on the annuitants of a Kenyan life insurance company by making use of the Lee carter model and further describes ways to manage this risk. The results of this paper are directly relevant to annuity providers. It is found that life expectancy is increasing in the future up to some point where it gradually decreases. Conclusions made are that several models should be used to investigate this risk so as to reduce model errors and that impact of the data used is financially material.. Suggestions are that companies should create Value at Risk estimates of capital to cover this risk over one year periods and that more research should be done on managing longevity risks by use of capital markets in the country.
Analysis of recurrent events with associated informative censoring: application to HIV data
(Strathmore University, 2020-06) Ejoku, Jonathan
In this study, we adapt a commonly used Cox-based model for recurrent events; the Prentice, Williams and Peterson Total -Time (PWP-TT) that has been largely used under the assumption of non-informative censoring and evaluate it under an informative censoring setting. Empirical evaluation was undertaken with the aid of the semi-parametric framework for recurrent events suggested by (Huang and Wang, 2004) where a subject speci c latent variable is used to model the association between the recurrent event and hazard of the failure time. All implementations were made in R Studio software, using the reReg package (Chiou and Huang, 2019) and the method in the reReg function set to 'cox.HW'. For validation we used HIV data from a typical HIV care setting in Kenya. Results show that the PWP-TT model generally t the data well, with a comparison to the Andersen-Gill method showing similar estimates, while the ordinary Cox model estimates were too unreliable
An Analysis of regional integration in a developing economy.
(Strathmore University, 2018) Oketch, Bruce Otieno
The purpose of this study is to find the effect of regional integration in the Kenyan economy with a particular emphasis of dete1mining whether the regional integration has resulted to trade creation or trade diversion. The study adopts an augmented gravity model to determine the effects of the regional integration and the resulting effects either being trade creation or trade diversion. Time series data was used for the period 1980-2015. Using a panel data analysis the results show that there was some trade creation within EAC and COMESA.
Analysis of risk measures in portfolio optimization for the Uganda Securities Exchange
(Strathmore University, 2021) Birungi, Criscent
For the most recent years, risk has become one of the essential parameters in portfolio optimization problems. Today most practitioners and researchers in portfolio optimization have used variance as a standard risk measure. This approach has been found subjective. The Markowitz (1952) mean-variance model considered variance as an adequate portfolio risk measure, and asset returns are multivariate normally distributed and that investors have a quadratic utility function which is subjective too. Other risk measures have been suggested to overcome the limitations of the mean-variance model. This paper analyzes which portfolio optimization models can better explain the optimal portfolio performance (high return, low risk) for the Uganda Security Exchange(USE). We compare Mean-Variance (MV), Mean Absolute Deviation (MAD), Robust Portfolios and Covariance Estimation Models( The Shrinked Mean-Variance (SMV) Models & Alternative Covariance Estimator (ACE) Models ) and Mean-Conditional Value-at-Risk (Mean-CVaR) models in terms of the risk and performance. Portfolios were developed by employing the MV, MAD, SMV, ACE and Mean-CVaR models. For the computed monthly returns and price data (February 2010 to January 2021) for USE selected stocks, we considered the results show that Mean-CVaR and ACE portfolios have the highest performance ratio compared to other models. We find that VaR is the best risk measure for portfolio optimization for the USE since it has lower values across all models than other risk measures. It is vital to consider all the available risk measures for a regulator or practitioner to make a good decision since using one can be subjective; as seen in our results, different risk measures yield different results.
An analysis of the absorption capacity of Official Development Assistance in Kenya from 1981 - 2010 and its relationship with economic development
(Strathmore University, 2015-11) Kipchirchir, Lang'at Douglas
One of the key components of development funds for Kenya is Official Development Assistance (ODA). However, given ODA's general underwhelming nature and overall ineffectiveness in fostering economic development, it would be useful to consider absorption capacity as the best measure of how well aid to Kenya is working, and not just the gross amount of ODA flows to Kenya. That is the basis of this research. The research utilized time series data obtained from the World Bank aggregator, using a time period of 30 years i.e. 1981 to 2010. The dependent variable in this research is GDP growth rate, which indexes economic development. The absorptive capacity was found to display a mean reverting trend, with an average of 87% over the past 30 years. Thereafter, an Auto regressive Distributed Lag model was used to determine the long run relationship between ODA absorption and economic development. The results of the model showed that the absorptive capacity of ODA negatively influences economic development in the current time period, but it has a positive and significant influence on economic development in the next time period. However, in the long run, the relationship between the two variables is statistically insignificant, meaning that the relationship between the two cannot be determined to be a result of anything but mere chance.
An analysis of the effect of investment climate on performance of public private partnerships - a case study of Sub Saharan Africa
(Strathmore University, 2015-12) Wainaina, Eric Mwangi
The study investigates the relationship between the performance of Public Private Partnerships (PPPs) and the investment climate in Sub Saharan Africa. The investment climate should significantly affect the performance of PPPs since good investment climate is a necessary prerequisite for investment. Infrastructure investments are essential to achieve economic prosperity, promoting growth and enhancing well-being. Recently to meet the growing demand for infrastructure development public entities have started to too).;_ at Public Private Partnerships to meet this deficit. The private sector participation is critical, bringing more funds; expertise and efficiency to the development of projects. For the analysis, a range of advanced panel estimators, namely random-Poisson, negative binomial, random generalized least square (GLS), random-tobit, were utilized to overcome the potential data related problems and for the robustness check of the estimated results. The results of the analysis suggest that large size and relatively higher income markets attract more PPP projects. The empirical evidence also suggests that macroeconomic stability, quality of regulation and governance are important factors in determining PPP in the infrastructure. The country risk is found to have some role in determining investment in PPPs although not to a very significant effect. The findings of this study will help the policymakers of developing countries in framing up such policies, so as to encourage more private firms to engage in infrastructure building through PPP.

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