-
English Premier League Scoreline Analysis: A Stochastic and Game Theory Approach
Ngonadi Lilian Oluebube,
Ezemma George Chijioke,
Etaga Harrison Oghenekevwe,
Ugoh Christogonus Ifeanyichukwu
Issue:
Volume 10, Issue 3, May 2021
Pages:
136-145
Received:
4 May 2021
Accepted:
24 May 2021
Published:
31 May 2021
Abstract: Making an appropriate decision in the selection of sustainable club from other clubs studied involves the use of right statistical approach, hence the need for stochastic and game theory analysis of English premier league scoreline. The following clubs Manchester United (MU), Chelsea (C), Arsenal (A), Manchester City (MC), Liverpool (LP), Tottenham (T) and Everton (E) were studied for both home and away matches for the period of 2010/2011 to 2019/2020 season. The optimal strategy and overall optimal strategy for MR G and MR B were obtained for each season and the 10 seasons respectively. The result showed that Manchester United has the highest probability (0.29) of being selected by MR B and Liverpool has the probability of 0.27 of being selected by MR G. The matrix of flow was also obtained when Manchester United played against Liverpool, given that Manchester United is home, as WWWLWWDWDD, and when Manchester United is away and Liverpool home, as WDLWLLDDWW. The two and four step transition matrix was also used to predict the future matches and their probabilities obtained given the probabilities of the previous game. The limiting distribution of the transition probability matrix obtained showed that Manchester United has a 67% chance of winning Liverpool while Liverpool has a 33% chance of winning Manchester United, this shows that Manchester United is stronger at home. Thus, the two most sustainable clubs out of the seven clubs studied are Manchester United and Liverpool.
Abstract: Making an appropriate decision in the selection of sustainable club from other clubs studied involves the use of right statistical approach, hence the need for stochastic and game theory analysis of English premier league scoreline. The following clubs Manchester United (MU), Chelsea (C), Arsenal (A), Manchester City (MC), Liverpool (LP), Tottenham...
Show More
-
Dependent Credit Default Risk Modelling Using Bernoulli Mixture Models
Misile Kunene,
Joseph Kyalo Mung’atu,
Euna Nyarige
Issue:
Volume 10, Issue 3, May 2021
Pages:
146-151
Received:
6 May 2021
Accepted:
24 May 2021
Published:
31 May 2021
Abstract: Generalized Linear Mixed Models (GLMMs) can be used to model the occurrence of defaults in a loan or bond portfolio. In this paper, we used a Bernoulli mixture model, a type of GLMMs, to model the dependency of default events. We discussed how Bernoulli mixture models can be used to model portfolio credit default risk, with the probit normal distribution as the link function. The general mathematical framework of the GLMMs was examined, with a particular focus on using Bernoulli mixture models to model credit default risk measures. We showed how GLMMs can be mapped into Bernoulli mixture models. An important aspect in portfolio credit default modelling is the dependence among default events, and in the GLMM setting, this may be captured using the so called random effects. Both fixed and random effects influence default probabilities of firms and these are taken as the systemic risk of the portfolio. After describing the model, we also conducted an empirical study for the applicability of our model using Standard and Poor’s data incorporating rating category (fixed effect) and time (random effect) as components of the model that constitute to the systemic risk of the portfolio. We were able to find the estimates of the model parameters using the Maximum Likelihood (ML) estimation method.
Abstract: Generalized Linear Mixed Models (GLMMs) can be used to model the occurrence of defaults in a loan or bond portfolio. In this paper, we used a Bernoulli mixture model, a type of GLMMs, to model the dependency of default events. We discussed how Bernoulli mixture models can be used to model portfolio credit default risk, with the probit normal distri...
Show More
-
Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model
Issue:
Volume 10, Issue 3, May 2021
Pages:
152-157
Received:
18 May 2021
Accepted:
11 June 2021
Published:
21 June 2021
Abstract: Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.
Abstract: Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which cau...
Show More
-
Poisson-Gamma and Spatial-Temporal Models: with Application to Cervical Cancer in Kenya’s Counties
Joseph Kuria Waitara,
Gregory Kerich,
John Kihoro,
Anne Korir
Issue:
Volume 10, Issue 3, May 2021
Pages:
158-166
Received:
1 June 2021
Accepted:
18 June 2021
Published:
26 June 2021
Abstract: In Africa, Cancer is an emerging health problem where in 2012 new cancer cases were about 847,00 and around 519,00 deaths, three quarters of those deaths occurred in sub-Saharan region. In 2018, cancer was ranked as the third leading cause of deaths in Kenya after infectious and cardiovascular diseases. In 2018 cancer incidences were estimated to be 47,887 new cancer cases and 32,987 deaths. According to data from World Health Organization in 2020, cervical cancer is the second most prevalent cancer among women while breast cancer is the first. In this study, data collected by the Nairobi Cancer Registry (NCR) was used to produce spatial-temporal distribution of the cervical cancer in counties in Kenya. The results showed that counties where data was available among them Embu, Meru, Machakos, Mombasa, Nyeri, Kiambu, Kakamega, Nairobi and Bomet respectively had high risk of cervical cancer. Availability of county-based estimates and spatial-temporal distribution of cervical cancer cases will aide development of targeted county strategies, enhance early detection, promote awareness and implementation of universal coverage of major control interventions which will be crucial in reducing and halting the rising burden of the cancer cases in Kenya. In counties where data was not available the model showed relative risks for cervical cancer disease was minute but it was present, therefore spatial temporal models are very appropriate to estimate relative risks of diseases even when there is a small sample (and possibly without a sample) in a given area by borrowing information from other neighboring regions.
Abstract: In Africa, Cancer is an emerging health problem where in 2012 new cancer cases were about 847,00 and around 519,00 deaths, three quarters of those deaths occurred in sub-Saharan region. In 2018, cancer was ranked as the third leading cause of deaths in Kenya after infectious and cardiovascular diseases. In 2018 cancer incidences were estimated to b...
Show More
-
Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data
Yeqian Liu,
James Plott,
Yingxiao Huang
Issue:
Volume 10, Issue 3, May 2021
Pages:
167-174
Received:
10 June 2021
Accepted:
23 June 2021
Published:
29 June 2021
Abstract: In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).
Abstract: In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to...
Show More
