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Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme
Ahmed Abo-Elmagd Soliman,
Essam Al-Sayed Ahmed,
Ahmed Hamed Abd Ellah,
Al-Wageh Ahmed Farghal
Issue:
Volume 3, Issue 6, November 2014
Pages:
167-176
Received:
21 September 2014
Accepted:
8 October 2014
Published:
20 October 2014
Abstract: Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.
Abstract: Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L...
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Statistical Analysis of Domestic Price Volatility of Sugar in Ethiopia
Anteneh Asmare Godana,
Yibeltal Arega Ashebir,
Tewodros Getinet Yirtaw
Issue:
Volume 3, Issue 6, November 2014
Pages:
177-183
Received:
26 August 2014
Accepted:
9 September 2014
Published:
30 October 2014
Abstract: The aim of this study was to model and identify determinants of monthly domestic price volatility of sugar in Ethiopia over the study period from December 2001 to December 2011 GC. The volatility in the domestic price of Sugar has been found to vary over months suggesting the use of GARCH family approach. Thus, family of special characteristics of time series models, namely ARCH, GARCH, TGARCH and EGARCH models with ARIMA mean equations were fitted to the data. The best fitting model among each family of models was selected based on how well the model captures the variation in the data and the optimal lag specification accessed via AIC and SBIC. Comparisons of the symmetric and asymmetric model were carried out based on the significance of asymmetric term in TGARCH and EGARCH models. The analysis showed that: statistically significance asymmetric term and least forecast error from the model established that EGARCH model with Student-t distributional assumptions for residual were superior to the GARCH and TGARCH models. Therefore, ARIMA (0,0,2)-EGARCH(1,3) with Student-t were chosen to be the best fitting models for monthly domestic price volatility of Sugar. Moreover, it was found that from candidate explanatory variables, import price for sugar, fuel oil price, exchange rate (dollar-birr), general inflation, inflation for non food items, inflation for food items, past shock, and volatility on monthly domestic price had statistically significant effect on the current month domestic price volatility on sugar.
Abstract: The aim of this study was to model and identify determinants of monthly domestic price volatility of sugar in Ethiopia over the study period from December 2001 to December 2011 GC. The volatility in the domestic price of Sugar has been found to vary over months suggesting the use of GARCH family approach. Thus, family of special characteristics of ...
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An Inquiry into the Distributional Properties of Reliability Rate
Issue:
Volume 3, Issue 6, November 2014
Pages:
197-201
Received:
24 October 2014
Accepted:
6 November 2014
Published:
20 November 2014
Abstract: The present paper attempts to model the maximum likelihood estimation of reliability rate and the related statistical properties. Reliability in general refers to the probability that a component or system is able to perform its function satisfactorily during a specific period under normal operating conditions. It is estimated as the fraction of time the unit/system is available for operation. For practical purposes, reliability rate is usually estimated using maximum likelihood estimator (MLE) from sample observations. No study has gone beyond this to analyze the statistical properties of the MLE of reliability rate; the present study is an attempt at such an inquiry. We derive the density function of reliability rate and also the moments; however, it is found that an evaluation of these two moments is very difficult as the series converge very slowly.
Abstract: The present paper attempts to model the maximum likelihood estimation of reliability rate and the related statistical properties. Reliability in general refers to the probability that a component or system is able to perform its function satisfactorily during a specific period under normal operating conditions. It is estimated as the fraction of ti...
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Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples
Mustafa Mohie El-Din,
Yahia Abdel-Aty,
Ahmed Shafay,
Magdy Nagy
Issue:
Volume 3, Issue 6, November 2014
Pages:
202-210
Received:
18 November 2014
Accepted:
28 November 2014
Published:
2 December 2014
Abstract: In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.
Abstract: In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample po...
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Modeling Export Price of Tea in Kenya: Comparison of Artificial Neural Network and Seasonal Autoregressive Integrated Moving Average
Mbiriri Ikonya,
Peter Mwita,
Anthony Wanjoya
Issue:
Volume 3, Issue 6, November 2014
Pages:
211-216
Received:
13 November 2014
Accepted:
21 November 2014
Published:
19 December 2014
Abstract: Agriculture sector is a key driver of economic growth in Kenya. It remains the main source of livelihood for the majority of the Kenyan people. Tea, coffee, and horticulture are the main agricultural exports in Kenya. Export price of these commodities fluctuates mainly due to law of demand and supply. Other reasons include; quality of goods and inflation effect on the dollar or other hard currencies. Further, farmers and their cooperative societies are affected by the local foreign exchange. The government and other stake holders require prior information on price trends for ease of planning. Thus it is important to forecast export prices of these commodities. The purpose of this study is to compare the forecasting performance of artificial neural network (ANN) model and a SARIMA model in export price of tea in Kenya. Secondary data was obtained from Kenya National Bureau of Statistics (KNBS). A total of 185 monthly export prices were obtained. A three layer feed-forward artificial neural network was trained using 70% of the data. The ANN model obtained was used to predict export prices for the remaining 30% of the data. SARIMA model was also used to predict export prices for the same duration. Forecasting performance was evaluated using Root mean squared errors (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). ANN demonstrated a superior performance over SARIMA model. The authors' ANN has high performance compared to SARIMA and can accurately predict export price of tea.
Abstract: Agriculture sector is a key driver of economic growth in Kenya. It remains the main source of livelihood for the majority of the Kenyan people. Tea, coffee, and horticulture are the main agricultural exports in Kenya. Export price of these commodities fluctuates mainly due to law of demand and supply. Other reasons include; quality of goods and inf...
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Estimation of Parameters of the Kumaraswamy Distribution Based on General Progressive Type II Censoring
Mostafa Mohie Eldin,
Nora Khalil,
Montaser Amein
Issue:
Volume 3, Issue 6, November 2014
Pages:
217-222
Received:
11 December 2014
Accepted:
22 December 2014
Published:
27 December 2014
Abstract: In this paper, we produced a study in Estimation for parameters of the Kumaraswamy distribution based on general progressive type II censoring. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters are obtained using the well known squared error loss (SEL) function. The findings are illustrated with actual and computer generated data.
Abstract: In this paper, we produced a study in Estimation for parameters of the Kumaraswamy distribution based on general progressive type II censoring. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters are obtain...
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Probability Model of Forward Birth Interval and Its Application
Issue:
Volume 3, Issue 6, November 2014
Pages:
223-227
Received:
16 December 2014
Accepted:
24 December 2014
Published:
6 January 2015
Abstract: In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and µ through derived model. The estimated values of λ and µ are 1.1051 and 2.841 respectively. The variance of estimated λ and µ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and µ is -0.026.With these estimates the expected frequencies for the distribution and χ2 = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.
Abstract: In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as...
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