School of Business & Public Management

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Author: search.filters.author.Simwa, Richard OHas files: Yes

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    On The Variation Of The Probability Distribution Of The Future Life–time: A Case Of The Kenyan Mortality Experience
    (Biometrics & Biostatistics International Journal, 2018) Simwa, Richard O
    A life table is an essential tool for valuing life insurance policies and it presents the probability distribution of the future life–time of a group of lives at the various ages. They are developed by the experts with actuarial knowledge. The life table will vary with the group of lives considered in the mortality investigation. Further the variation may also prevail when the same group of lives is investigated at different time periods, due to the effect of generational change in mortality. In this paper we apply statistical inference on published life tables for the Kenyan mortality experience for the mortality investigations performed during two separate disjoint time periods, to investigate significance of the variation in the mortality as the periods of the investigation vary. It is shown that the variation in the probability distribution of the future life–time for the Kenyan mortality experience is significant. Thus we confirm, as known in practice by the actuaries, that there is a need for continuous mortality investigations and the construction of the corresponding life tables, every after some time interval, to account for the variation in mortality as generations vary.
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    Approximations of ruin probabilities under financial constraints
    (Applied Mathematical Sciences, 2022) Simwa, Richard O; Odiwuor, Calvine O; Onyango, Fredrick
    In this paper, we investigate the approximate ruin probabilities un-der financial constraints (interest rate, inflation, and taxation). We formulate a risk process whose premium inflow is influenced by the economic effects of inflation and interest rate. Thereafter we invokethe Albrecher-Hipp loss-carried-forward tax scheme from which an ex-act formula for the ruin probability for exponentially distributed claimsis derived. Finally, an explicit asymptotic formula when the claims have sub-exponential distribution is also derived using the Pollaczek-Khintchine formula.
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    On stock returns volatility and trading volume of the Nairobi securities exchange index
    (RMS: Research in Mathematics &Statistics, 2021) Simwa, Richard O; Mwaniki, Joseph I; Kalovwe, Sebastian K
    This study attempts to put forward a framework that can be utilized to model the dynamics of the underlying returns on asset. The intention is to probe the dynamic connection between volatility of stock returns and trading volume of the Nairobi Securities Exchange (NSE20) index. The consequence of incorporating trading volume in the equation for conditional variance of the generalized autoregressive conditional heteroscedasticity (GARCH) model on volatility persistence is investigated. Further, this study brings into play GARCH, GARCH-M, and EGARCH models conditioned to normal, student-t and generalized error distributions to model the dynamic structure of the NSE20 index for the period 2 January 2001 to 31 December 2017. The results disclose some well-known stylized facts of returns on stock, for instance, volatility clustering, heavy tails, leverage effects, and leptokurtic distribution. The estimates of parameters of the three models, that is, GARCH (1, 1), GARCH-M (1, 1), and EGARCH models report that the correlation between stock returns volatility and trading volume is positive and statistically significant. Moreover, estimates of the coefficients of EGARCH (1, 1) model report an increased measure of persistence on volatility as well as volatility asymmetry and the absence of leverage effect in the returned volatility. Also, the estimates of GARCH (1, 1) and GARCH-M (1, 1) parameters report that volatility persistence dwindles after trading volume is incorporated in the equation for the conditional variance.
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    Bayesian Model Averaging in Modeling of State Specific Failure Rates in HIV/AIDS Progression
    (Mathematics and Statistics, 2022) Simwa, Richard O; Mwirigi, Nahashon; Wainaina, Mary; Sewe, Stanley
    In modeling HIV/AIDS progression, we carried out a comprehensive investigation into the risk factors for state-specific-failure rates to identify the influential co-variates using Bayesian Model averaging method (BMA). BMA provides a posterior probability via Markov Chain Monte Carlo (MCMC) for each variable that belongs to the model. It accounts for model uncertainty by averaging all plausible models using their posterior probabilities as the weights for model-averaged predictions and estimates of the required parameters. Patients' age, and gender, among other co-variates, have been found to influence the state-specific-failure rates highly. However, the impact of each of the factors on the state specific-failure was not quantified. This paper seeks to evaluate and quantify the contribution of the patient's age and gender, CD4 cell count during any two consecutive visits, and state movement on the state-specific-failure rates for patients transiting either to the same, better or worse state. We used R Studio statistical Programming software to implement the method by applying BMS and BMA packages. State movement had a comparatively large coefficient with a posterior inclusion probability (PIP) of 0.8788 (87.88%). Hence, the most critical variable followed by observation-two-CD4-cell-count with a PIP of 0.1416 (14.16%), age and gender were the last with a PIP of 0.0556 (5.56%) and 0.0510 (5.10%) respectively for patients transiting to the same state. For patients transiting to a better state, the patients' age group dominated with a PIP of 0.9969 (99.69%), followed by patients' gender with a PIP of 0.0608 (6.08%). Patients' CD4 cell count during the second observation had the least PIP of 0.0399 (3.99%). For patients transiting to a worse disease state, patients CD4 cell count during the second observation proved to be the most important, with a PIP of 0.6179(61.79%) followed by state movement with a PIP of 0.2599 (25.99%), patients gender tailed with a PIP of 0.0467 (4.67%).
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    Weibull Distribution as the Choice Model for State-Specific Failure Rates in HIV/AIDS Progression
    (Mathematics and Statistics, 2022) Simwa, Richard O; Wainaina, Mary; Sewe, Stanley; Mwirigi, Nahashon
    This study considered the problem of selecting the best single model for modeling state-specific failure rates in HIV/AIDS progression for patients on antiretroviral therapy with age and gender as risk factors using exponential, twoparameter, and three-parameter Weibull distributions. CD4 count changes in any two consecutive visits, the mean waiting time (μ), and transitional rates (λ) for remaining in the same state or transiting to a better or a worse state were analyzed. Various model selection criteria, namely, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Log-Likelihood (LL), were used in each specific disease state. The Maximum Likelihood Estimation (MLE) method was applied to obtain the parameters of the distributions used. Plots of State-specific transition rates (λ) depicted constant, increasing, decreasing, and unimodal trends. Three-parameter Weibull distribution was the best for male patients and patients aged (40-69) years transiting in the states 1-2, 3-4, and 4-5, and 1-2, 3-4, and 5-6, respectively, and for male, female patients, and patients aged (40-69), remaining in the same state. Two-parameter Weibull distribution was the best for female patients and patients aged (20-39) years transiting in the states 1-2, 2-3, 4-5, and 1-2, 2-3, 3-4, respectively. Exponential distribution proved inferior to the other two distributions used.
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    On regime-switching European option pricing
    (Taylor & Francis, 2023) Simwa, Richard O; Mwaniki, Joseph I; Kalovwe, Sebastian K
    The concern of this article is to derive a regime switching model that can be utilized to price European call options for a financial market that exhibits structural changes with time. The model is formulated based on the fact that the underlying asset process is described by a geometric Brownian motion that is modulated by a continuous-time Markov chain with two regimes. Moreover, by an application of the change of measure technique, an option price is derived under the risk neutral valuation and the model parameter estimates is performed by use of the maximum likelihood estimation. The model implementation is carried out by utilizing the Russell 2000 and Facebook in dices data sets. The model results are compared with that of the Black-Scholes model in order to establish the model with better results in terms of predicting the European call option prices. In general, the data sets have common characteristics of financial time series across the regimes and the volatility process spends longer time in regime 2 than it stays in regime 1. The predicted call option prices from both models are more or less similar across the market indices; however, the results of the Black-Scholes model are a bit closer to the market prices than that of the regime-switching model across the two markets. Therefore, the Black-Scholes model slightly gives better results for the Russell 2000 and Facebook indices data sets as compared with the RS model.
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    A comparison of two sample approaches to regression calibration for measurement error correction
    (International Journal of Statistics and Applied Mathematics, 2023) Kamun, Samuel J; Nyakundi, Cornelious; Simwa, Richard O
    This study compares ways for improving regression calibration. This is a method for combining two samples in order to reduce measurement error and improve the relative efficiency of linear regression models. Since two or more samples are more likely than a single sample to accurately represent the population under study, two samples are used in regression calibration to produce a realistic picture of the actual population. In this investigation, we compared independent estimates derived from two samples using a weight equal to the reciprocal of the estimated sampling probability. The study also examined the estimations produced after combining the two datasets into one, and modified the weight of each sample unit accordingly. The most typical application of regression calibration methods is to account for bias in projected responses induced by measurement inaccuracies in variables. Because of its simplicity, this method is commonly utilized. The conditional expectation of the genuine response is estimated using regression calibration, given that the predictor variables are measured with error and the other covariates are assessed without error. Instead of the unknown genuine response, predictors are estimated and used to examine the link between response and result. Regression calibration programs necessitate extensive knowledge of unobservable true predictors. This information is frequently collected from validation studies that employ unbiased measurements of true predictors. The results of two sample strategies were employed and compared in this study. Device fault, laboratory mistake, human error, difficulty documenting or completing measurements, self-reported errors, and intrinsic vibrations of the underlying instrument can all cause measurement inaccuracies. Covariate measurement error has three consequences: In addition to obscuring data features and making graphical model analysis more difficult, estimates of statistical model parameters might be skewed, and effectiveness in detecting correlations between variables can be severely impaired. This study's two sampling procedures produced satisfactory results.
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    Two Sample Approaches to Regression Calibration for Measurement Error Correction
    (International Journal of Statistical Distributions and Applications, 2023) Kamun, Samuel J; Nyakundi, Cornelious; Simwa, Richard O
    The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes-significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.