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Characterization of the Linear Failure Rate Distribution by General Progressively Type-II Right Censored Order Statistics
M. M. Mohie El-Din,
A. Sadek,
Marwa M. Mohie El-Din,
A. M. Sharawy
Issue:
Volume 6, Issue 3, May 2017
Pages:
129-140
Received:
4 March 2017
Accepted:
20 March 2017
Published:
11 April 2017
Abstract: In this article, we establish recurrence relations among single moments and among product moments of general progressively Type-II right censored order statistics and characterization for linear failure rate distribution using recurrence relations of single moments and product moments of general progressively Type-II right censored order statistics. Further, the results are specialized to the progressively Type-II right censored order statistics.
Abstract: In this article, we establish recurrence relations among single moments and among product moments of general progressively Type-II right censored order statistics and characterization for linear failure rate distribution using recurrence relations of single moments and product moments of general progressively Type-II right censored order statistics...
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Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm
Joseph Nderitu Gitahi,
John Kung’u,
Leo Odongo
Issue:
Volume 6, Issue 3, May 2017
Pages:
141-149
Received:
16 March 2017
Accepted:
6 April 2017
Published:
27 April 2017
Abstract: This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as well as the asymptotic variance-covariance matrix. By using the obtained variance-covariance matrix of the MLEs, the asymptotic 95% confidence interval for the parameters are constructed. Through simulation, the behavior of these estimates are studied and compared under different censoring schemes and parameter values. It is concluded that for an increasing sample size; the estimated value of the parameters converges to the true value, the variances decrease and the width of the confidence interval become narrower.
Abstract: This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as w...
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Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study
Winnie Mbusiro Chacha,
P. Mwita,
B. Muema
Issue:
Volume 6, Issue 3, May 2017
Pages:
150-155
Received:
28 October 2015
Accepted:
6 November 2015
Published:
22 May 2017
Abstract: Value at Risk (VaR) became the industry accepted measure for risk by financial institutions and their regulators after the Basel I Accords agreement of 1996. As a result, many methodologies of estimating VaR models used to carry out risk management in finance have been developed. Engle and Manganelli (2004) developed the Conditional Autoregressive Value at Risk (CAViaR) which is a quantile that focuses on estimating and measuring the lower tail risk. The CAViaR quantile measures the quantile directly in an autoregressive framework and applies the quantile regression method to estimate the CAViaR parameters. This research applied the asymmetric CAViaR, symmetric CAViaR and Indirect GARCH (1, 1) specifications to KQ, EABL and KCB stock returns and performed a set of in sample and out of sample tests to determine the relative efficacy of the three different CAViaR specifications. It was found that the asymmetric CAViaR slope specification works well for the Kenyan stock market and is best suited to estimating VaR. Further, more research needs to be carried out to develop e a satisfactory VaR estimation model.
Abstract: Value at Risk (VaR) became the industry accepted measure for risk by financial institutions and their regulators after the Basel I Accords agreement of 1996. As a result, many methodologies of estimating VaR models used to carry out risk management in finance have been developed. Engle and Manganelli (2004) developed the Conditional Autoregressive ...
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On a New Class of Regular Doubly Stochastic Processes
Reza Farhadian,
Nader Asadian
Issue:
Volume 6, Issue 3, May 2017
Pages:
156-160
Received:
17 March 2017
Accepted:
29 March 2017
Published:
25 May 2017
Abstract: In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.
Abstract: In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagona...
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Modelling and Forecasting Inflation Rate in Kenya Using SARIMA and Holt-Winters Triple Exponential Smoothing
Issue:
Volume 6, Issue 3, May 2017
Pages:
161-169
Received:
5 April 2017
Accepted:
13 April 2017
Published:
25 May 2017
Abstract: In this paper, two models of forecasting are used the Box-Jenkins procedure employing the SARIMA and the Holt-Winters triple exponential smoothing. Published Consumer Price Index Data from Kenya National Bureau of Statistics (KNBS) for the period November 2011 to October 2016 was used. This paper we equate the forecasted values of both the models and we choose the best model based on the least mean Absolute square error (MASE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The three step model building for Box-Jenkins was first employed, followed by the Hold-Winters triple exponential smoothing. The study found the SARIMA Model was a better model than the Holt-winters triple exponential smoothing as per the obtained results using MASE, MAE and MAPE.
Abstract: In this paper, two models of forecasting are used the Box-Jenkins procedure employing the SARIMA and the Holt-Winters triple exponential smoothing. Published Consumer Price Index Data from Kenya National Bureau of Statistics (KNBS) for the period November 2011 to October 2016 was used. This paper we equate the forecasted values of both the models a...
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Logistic Mixed Modelling of Determinants of International Migration from the Southern Ethiopia: Small Area Estimation Approach
Tsedeke Lambore Gemecho,
Ayele Taye Goshu
Issue:
Volume 6, Issue 3, May 2017
Pages:
170-182
Received:
29 March 2017
Accepted:
15 April 2017
Published:
27 May 2017
Abstract: The main objective of this study is to investigate socio-demographic and economic characteristics of a household on international migration and to estimate small area proportions at district and enumeration area level. Migration status refers to whether a household has at least one member who ever migrated abroad or not. A total of 2288 data are collected from sixteen randomly sampled districts in Hadiya and Kembata-Tembaro zonal areas, Southern Ethiopia. Several versions of the binary logistic mixed models, as special cases of the generalized linear mixed model, are analyzed and compared. The findings of the study reveal that about 39.4% of the households have at least one international migrant, and the rest 60.6% have no such migrants. Based on analysis of the generalized linear model and stepwise variable selection, four predictors are found to be significantly related to household migration status at 5% significance level. These are age, occupation, and educational level of household head and family size. Then twelve mixed models are analyzed and compared. The best fitting model to the data is found to be the logistic mixed regression model consisting of the six predictors with age nested within districts as random effects. Area or district specific random effect has variance of 1.6180. The district level random variation founded on final model with six predictor variables about the presence of migrant in the households such as the variation between districts is 33% and variation within the district is 67%. From analysis of the final model, it is found that the likelihood of a household of having international migrant increases with head's age and family size. An increase of family size by one person increases the log odds of having migrant by 0.131 indicating that large family size is one of the determinants for migration in the study area. The migration prevalence varies among the zones, the districts and the enumeration areas. Household characteristics: age, educational level and occupation of head, and family size are determinants of international migration. Community based intervention is needed so as to monitor and regulate the international migration for the benefits of the society.
Abstract: The main objective of this study is to investigate socio-demographic and economic characteristics of a household on international migration and to estimate small area proportions at district and enumeration area level. Migration status refers to whether a household has at least one member who ever migrated abroad or not. A total of 2288 data are co...
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