by Taruna Kumari and Anupam Pathak
Original Research
In this article, we consider a multicomponent stress-strength model which has k independent and identical strength components X1, X2, …, Xk and each component is exposed to a common random stress Y. Both stress and strength are assumed to have proportional hazard rate model with different unknown power parameters. The system is regarded as operating only if at least s out of k(1≤s≤k) strength variables exceeds the random stress. Reliability of the system is estimated by using maximum likelihood, uniformly minimum variance unbiased and Bayesian methods of estimation. The asymptotic confidence interval is constructed for the reliability function. The performances of these estimators are studied on the basis of their mean squared error through Monte Carlo simulation technique.
American Journal of Applied Mathematics and Statistics. 2019, 7(4), 152-160. DOI: 10.12691/ajams-7-4-5
Pub. Date: July 29, 2019
8295 Views1569 Downloads
by Charlotte K Mokaya and DR. Edward Gachangi Njenga
Original Research
The main objective of this study was to derive a nonparametric estimator for the variance of the population mean when the population structure is nonlinear and heteroscedastic. Therefore, this paper sought to investigate the performance of Nadaraya-Watson estimator with a variable bandwidth. The methodology was derived by modifying the Nadaraya-Watson estimator where the bandwidth was a function of the range of observations. The performance of the proposed estimator was compared with other estimators i.e. Ratio estimator and Nadaraya-Watson with a fixed bandwidth. To measure performance of each of the estimators, average mean squared error was considered. It was found out that the Ratio estimator performs well for linear and homoscedastic populations while the Nadaraya-Watson with fixed bandwidth performs well for nonlinear and heteroscedastic populations. However, in the light of these findings, Nadaraya-Watson estimator (with variable bandwidth) was found to perform better and most efficient than the Ratio estimator and Nadaraya-Watson estimator (with fixed bandwidth) in nonlinear and heteroscedastic populations. It was also found to be the most robust compared to the estimators considered in this study.
American Journal of Applied Mathematics and Statistics. 2019, 7(4), 146-151. DOI: 10.12691/ajams-7-4-4
Pub. Date: July 01, 2019
7995 Views917 Downloads1 Likes
by Amon kiregu, Anthony Waititu and Antony Ngunyi
Original Research
This research paper use PELT algorithm and GARCH models to conduct volatility change point analysis and to model and forecast change point in volatility of USD/KES data. This study employed simulated data and data from Central Bank of Kenya for the period between January 2005 to December 2018. The estimates and actual values of change points in volatility did not differ after analysis. The USD/KES data exhibited volatility clustering in some time periods. The volatility adjusted GARCH models outperformed plain models. The simulated estimates of GARCH models were almost converging to the parameters from USD/KES data using the same models. The GARCH models that incorporate change points registered better forecasting performance compared to the plain models. The PGARCH, TGARCH and GJRGARCH models had the same forecasting performance measures in absence and presence of change points. The study recognized TGARCH (1,1) as the best model for modelling and forecasting. Banks can use univariate GARCH models in conjunction with PELT algorithm to track loan defaulters. Hospitals can use the same technique to determine the most recurring diseases. Companies can apply the same to determine abnormal profits and losses. The technique can be applied in other sectors like in meteorology.
American Journal of Applied Mathematics and Statistics. 2019, 7(4), 138-145. DOI: 10.12691/ajams-7-4-3
Pub. Date: June 24, 2019
10788 Views1437 Downloads1 Likes
by G. Srinivasa Rao, K. Rosaiah and S. V. S. V. S. V. Prasad
Original Research
This article describes the development of an acceptance sampling plan based on percentiles for Type-II generalized log-logistic distribution (TGLLD) introduced by Rosaiah et. al. [1]. The plan is developed by considering the lifetime percentiles as a variable and the life test will be terminated at a pre-specified time. The objective of the test is to determine the minimum sample size required to achieve a specific lifetime percentile at an acceptable level of consumer and producer risks. Determined the OC values and are presented along with producer risks. The sustainability of the plan is illustrated with real data set.
American Journal of Applied Mathematics and Statistics. 2019, 7(4), 131-137. DOI: 10.12691/ajams-7-4-2
Pub. Date: June 21, 2019
7513 Views1493 Downloads
by Joseph Dongho and Sim¨¦on Kemmegne Fopossi
Original Research
Given a regular Euclidean pyramid with square base, we use basic properties of great circle associated to it sides to prove the existence of its spherical counterpart. We also prove that its homeomorphic to its spherical counterpart.
American Journal of Applied Mathematics and Statistics. 2019, 7(4), 120-130. DOI: 10.12691/ajams-7-4-1
Pub. Date: June 04, 2019
7894 Views1357 Downloads