Many sampling methods have been suggested for estimating the population median. In the situation when the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to the simple random sampling. In this paper, the superiority of several ranked set sampling methods over the simple random sampling are illustrated through some simulation study. In addition, some new research topics under ranked set sampling are suggested.
Climate changes have become serious issues that have been widely discussed by researchers. One of the issues concerns with the study in changes of rainfall patterns. Changes in rainfall patterns affect the dryness and wetness conditions of a region. In this study, the three-dimensional loglinear model was used to fit the observed frequencies and to model the expected frequencies of wet class transition on eight rainfall stations in Peninsular Malaysia. The expected frequency values could be employed to determine the odds value of wet classes of each station. Further, the odds values were used to estimate the wet class of the following month if the wet class of the previous month and current month were identified. The wet classification based on SPI index (Standardized Precipitation Index). For station that was analyzed, there was no difference found were between estimated and observed wet classes. It was concluded that the loglinear models can be used to estimate the wetness classes through the estimates of odds values.
Long-memory is often observed in time series data. The existence of long-memory in a data set implies that the successive data points are strongly correlated i.e. they remain persistent for quite some time. A commonly used approach in modellingthe time series data such as the Box and Jenkins models are no longer appropriate since the assumption of stationary is not satisfied. Thus, the scaling analysis is particularly suitable to be used for identifying the existence of long-memory as well as the extent of persistent data. In this study, an analysis was carried out on the observed daily mean per hour of ozone concentration that were available at six monitoring stations located in the urban areas of Peninsular Malaysia from 1998 to 2006. In order to investigate the existence of long-memory, a preliminary analysis was done based on plots of autocorrelation function (ACF) of the observed data. Scaling analysis involving five methods which included rescaled range, rescaled variance, dispersional, linear and bridge detrending techniques of scaled windowed variance were applied to estimate the hurst coefficient (H) at each station. The results revealed that the ACF plots indicated a slow decay as the number lag increased. Based on the scaling analysis, the estimated H values lay within 0.7 and 0.9, indicating the existence of long-memory in the ozone time series data. In addition, it was also found that the data were persistent for the period of up to 150 days.
McIntyre was the first to suggest ranked set sampling (RSS) method for estimating the population mean. In this paper, we modify RSS to come up with new sampling method, namely, two stage ranked set sampling (TSRSS) for samples of size m=3k (k=1,2,..). The TSRSS is suggested for estimating the population median in order to increase the efficiency of the estimators. The TSRSS was compared to the simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS), median ranked set sampling (MRSS) and balance groups ranked set sampling (BGRSS) methods. It is found that, TSRSS gives an unbiased estimator of the population median of symmetric distributions and it is more efficient than SRS. Also, it is more efficient than RSS, ERSS, MRSS and BGRSS based on the same number of measured units. For asymmetric distributions considered in this study, TSRSS has a small bias and smaller variance than SRS, RSS, ERSS, MRSS and BGRSS methods.
The presence of extra zeros is commonly observed in traffic accident count data. Past research opt to the zero altered models and explain that the zeros are sourced from under reporting situation. However, there is also an argument against this statement since the zeros could be sourced from Poisson trial process. Motivated by the argument, we explore the possibility of mixing several discrete distributions that can contribute to the presence of extra zeros. Four simulation studies were conducted based on two accident scenarios and two discrete distributions: Poisson and negative binomial; by considering six combinations of proportion values correspond to low, moderate and high mean values in the distribution. The results of the simulation studies concur with the claim as the presence of extra zeros is detected in most cases of mixed Poisson and mixed negative binomial data. Data sets that are dominated by Poisson (or negative binomial) with low mean show an apparent existence of extra zeros although the sample size is only 30. An illustration using a real data set concur the same findings. Hence, it is essential to consider the mixed discrete distributions as potential distributions when dealing with count data with extra zeros. This study contributes on creating awareness of the possible alternative distributions for count data with extra zeros especially in traffic accident applications.
Statistical distributions of annual extreme (AE) and partial duration (PD) for rainfall events are analysed using a database of 50 rain-gauge stations in Peninsular Malaysia, involving records of time series data which extend from 1975 to 2004. The generalised extreme value (GEV) and generalised Pareto (GP) distributions are considered to model the series of annual extreme and partial duration. In both cases, the three parameter models such as GEV and GP distributions are fitted by means of L-moments method, which is one of the commonly used methods for robust estimation. The goodness-of-fit of the theoretical distribution to the data is then evaluated by means of L-moment ratio diagram and several goodness-of-fit (GOF) tests for each of the 50 stations. It is found that for the majority of stations, the AE and PD series are well fitted by the GEV and GP models, respectively. Based on the models that have been identified, we can reasonably predict the risks associated with extreme rainfall for various return periods.
Kajian ini bertujuan untuk memetakan kes kemortalan bayi mengikut daerah di Semenanjung Malaysia bagi tahun 1991 hingga 2000. Penganggaran risiko relatif berdasarkan kaedah Bayes empirik telah digunakan dalam kajian ini. Tiga kaedah penganggaran parameter dihuraikan iaitu kaedah momen, kaedah kebolehjadian maksimum dan kaedah penganggaran gabungan momen dan kebolehjadian maksimum. Keteguhan anggaran parameter yang diperoleh diuji menggunakan kaedah Bootstrap. Hasil kajian mendapati jurang antara kawasan berisiko rendah dengan kawasan berisiko tinggi adalah lebih besar pada awal dekad 2000 berbanding pada awal dekad 1990-an walaupun pada dasarnya kadar mortaliti bayi secara keseluruhannya adalah semakin berkurangan pada peringkat nasional. Kawasan pantai timur Semenanjung Malaysia masih pada takuk yang sama iaitu masih berada dalam kategori berisiko tinggi sepanjang tempoh yang dikaji. Seterusnya, gambaran terdapatnya tompokan risiko juga turut terpapar dalam peta yang dihasilkan. Berdasarkan kaedah Bootstrap, parameter-parameter yang dianggarkan dalam kajian ini adalah teguh.