Rainfall is an interesting phenomenon to investigate since it is directly related
to all aspects of life on earth. One of the important studies is to investigate and under-
stand the rainfall patterns that occur throughout the year. To identify the pattern, it
requires a rainfall curve to represent daily observation of rainfall received during the year.
Functional data analysis methods are capable to convert discrete data intoa function that
can represent the rainfall curve and as a result, try to describe the hidden patterns of the
rainfall. This study focused on the distribution of daily rainfall amount using functional
data analysis. Fourier basis functions are used for periodic rainfall data. Generalized
cross-validation showed 123 basis functions were sufficient to describe the pattern of daily
rainfall amount. North and west areas of the peninsula show a significant bimodal pattern
with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-
modal patterns that reached a peak in the last three months. Southern areas show more
uniform trends throughout the year. Finally, the functional spatial method is introduced
to overcome the problem of estimating the rainfall curve in the locations with no data
recorded. We use a leave one out cross-validation as a verification method to compare
between the real curve and the predicted curve. We used coefficient of basis functions
to get the predicted curve. It was foundthatthe methods ofspatial prediction can match
up with theexistingspatialpredictionmethodsin terms of accuracy,but it isbetterasthe new
approach provides a simpler calculation.
This paper is an attempt to perceive and order guns using a two-layer neural system model taking into account a feedforward backpropagation calculation. Numerical properties from the joined pictures were utilised for enhanced gun characterisation execution. Inputs of the system model were 747 pictures blackmailed from the discharging pin impression of five differing guns model, Parabellum Vector SPI 9mm. Components created from the dataset were further grouped into preparation set (523 components), testing set (112 components) and acceptance set (112 components). Under managed learning, exact results exhibited that a two-layer BPNN of 11-11-5 arrangement, with tansig/purelin exchange capacities and a “trainlm” preparing calculation, had productively delivered 87% right aftereffect of grouping. The order result serves to be progressed and contrasted with the previous works. Finally, the joined picture districts can offer some accommodating data on the grouping of gun.
This study attempts to trace changes in the wet spells over Peninsular Malaysia based on the daily rainfall data from 32 selected rainfall stations which include four sub-regions; northwest, west, south and east, for the period of 1975 to 2004. Six wet spells indices comprising of the main characteristics (maximum, mean, standard deviation), the persistency of two consecutive wet days and the frequency of the short and long duration of wet spells will be used to identify whether or not these indices increase or decrease over Peninsular Malaysia during the monsoon seasons. The study indicates that the eastern areas of the peninsula could be considered as the wettest areas since almost all the indices of wet spells over these areas are higher than over the other regions during the northeast monsoon (NE). The Mann-Kendall (MK) trend test revealed that almost all of the stations located in the eastern areas of the peninsula exhibited a positive trend in the mean, variability and persistency of wet spells indices during the NE monsoon, while a negative trend was observed during the southwest monsoon (SW) in these areas. Moreover, these indices showed a positive trend, and at the same time a decreasing trend was observed in the frequency of the long wet spells in most stations located over the west coast of Peninsular Malaysia during the SW monsoon for the period of 1975 to 2004.
Rainfalls data have been broadly used in researches including in hydrological and meteorological areas. Two common ways in extracting observations from hourly rainfalls data are the window-based analysis (WBA) and storm-event analysis (SEA) approach. However, the differences in the qualitative and quantitative properties of both methods are still vaguely discussed. The aim of studying these dissimilarities is to understand the effects of each approach in modelling and analysis. The qualitative difference is due to the way the two analyses define the accumulated rainfalls for observations which are referred to as rainfall and storm depths, respectively. The repetitiveness of rainfall depths provide nested structure while the storm depths are considered independent. The quantitative comparisons include their statistical and scaling properties that are linked by the self-similarity concept from simple scaling characteristics. If self-similarity concept
holds, then the rainfall or storm depths follow simple scaling and the analysis would be simplified. The rainfall depths showed clearer simple scaling characteristics compared to the storm depths. Though the storm depths do not yield self-similarity for a large range of storm duration but the characteristics of simple scaling can be observed for a reduced range of the considered duration. In general, the context of the research and the region of the time interval and duration will be an important aspects to consider in choosing which method is best to use for analyzing the data.
This paper presents various imputation methods for air quality data specifically in Malaysia. The main objective was to
select the best method of imputation and to compare whether there was any difference in the methods used between stations
in Peninsular Malaysia. Missing data for various cases are randomly simulated with 5, 10, 15, 20, 25 and 30% missing.
Six methods used in this paper were mean and median substitution, expectation-maximization (EM) method, singular
value decomposition (SVD), K-nearest neighbour (KNN) method and sequential K-nearest neighbour (SKNN) method. The
performance of the imputations is compared using the performance indicator: The correlation coefficient (R), the index
of agreement (d) and the mean absolute error (MAE). Based on the result obtained, it can be concluded that EM, KNN
and SKNN are the three best methods. The same result are obtained for all the eight monitoring station used in this study.
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.
This study suggests the regression models of Lognormal, Normal and Gamma for the construction of an insurance scoring system. Comparison between Lognormal, Normal and Gamma regression models were also carried out, and the comparison were centered upon three main elements; fitting procedures, parameter estimates and structure of scores. The main advantage of utilizing a scoring system is that the system may be used by insurers to differentiate between good and bad insureds and thus allowing the profitability of insureds to be predicted.
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.
Keputusan terakhir yang dicari dalam menyelesaikan masalah berbilang kriteria ialah satu pangkat kedudukan unit yang dianalisis berdasarkan prestasi keseluruhan unit-unit tersebut. Satu cara untuk mendapatkan prestasi keseluruhan setiap unit adalah dengan menggabungkan prestasi dan wajaran kriteria masing-masing melalui pelbagai kaedah pengagregatan. Kajian tertumpu kepada penerapan tiga kaedah asas pangkat dalam menilai kepentingan kriteria yang melibatkan satu panel penilai dengan kewibawaan berbeza. Hanya dua pendekatan pengagregatan berasaskan kaedah pemurataan tertib berpemberat sesuai diutarakan agar hasil akhir boleh dicapai. Setiap pendekatan pengagregatan yang dicadangkan diringi dengan contoh pengiraan.
Oleh sebab kejadian jenayah bersenjata api semakin berleluasa, pengecaman senjata api yang digunakan oleh penjenayah amat diperlukan sebagai bahan bukti dalam mahkamah. Beberapa sistem pengecaman senjata api telah diutarakan sebagai pengganti kepada cara penyiasatan tradisional yang amat bergantung kepada kepakaran ahli balistik. Pemetakan rantau tumpuan (ROI) berdasarkan kedudukan titik sauh (PAP) sempadan bulatan kesan pin peletup pada tapak kelongsong peluru merupakan langkah yang amat penting dalam sistem pengecaman senjata api automatik. Walau bagaimanapun, kaedah yang digunakan dalam kajian lepas bagi mengesan PAP sempadan bulatan tersebut adalah sangat kompleks dan memerlukan masa pemprosesan yang panjang. Kajian ini menerokai algoritma yang efisien dan berkemampuan untuk mengesan PAP sempadan bulatan secara automatik. Algoritma yang diutarakan merupakan gabungan daripada penapis penajaman reruang, penormalan histogram, pengambangan dan penganggar kuasa dua terkecil tak berpemberat. Dua kaedah pengambangan yang terkenal telah diuji dan dibandingkan, iaitu kaedah pengambangan berasaskan pengelompokan dan kaedah berasaskan entropi. Di samping itu, penerokaan kesan saiz dan bentuk ROI terhadap kadar pengelasan senjata api turut dipersembahkan. Sebanyak 747 imej kesan pin peletup jenis sempadan bulatan peletup yang dihasilkan oleh lima pucuk pistol yang berlainan daripada jenis yang sama digunakan untuk menguji algoritma yang diutarakan. Kadar pengelasan imej kesan pin peletup yang memberangsangkan (> 95%) telah dicapai dengan algoritma yang dicadangkan. Kajian juga mendapati bahawa saiz dan bentuk pemetakan ROI mempunyai kesan langsung terhadap kadar pengelasan senjata api.
This study investigated the spatial pattern and trends of the daily rainfall data in Peninsular Malaysia based on seasonal rainfall indices. Five rainfall indices which describe the main characteristics of rainfall, the total amount of rainfall, frequency of wet days, rainfall intensity, extreme frequency, and extreme intensity, were employed in this study. The statistics of rainfall indices were calculated in terms of their means for four regions in Peninsular Malaysia for the period 1975 to 2004. The findings indicate that the southwest monsoon had the greatest impact on the western part of the Peninsula, particularly in characterizing the rainfall pattern of the northwest region. During this season, the northwest region could be considered as the wettest region since all rainfall indices tested are higher than in other regions of the Peninsula. Otherwise, the northwest region is denoted as the driest part of the Peninsula during the northeast monsoon period. The northwest region is less influenced by the northeast monsoon because of the existence of the Titiwangsa Range, which blocks the region from receiving heavy rainfall. On the other hand, it is found that the lowlands areas such as the eastern part of the Peninsula are strongly characterized by the northeast monsoonal flow. Based on the results of the Mann-Kendall test, as the trend of the total amount of rainfall and the frequency of wet days during the southwest monsoon decrease at most of the stations, the rainfall intensity increases. In contrast, increasing trends in both the total amount of rainfall and the frequency of wet days were observed at several stations during the northeast monsoon, which give rise to the increasing trend of rainfall intensity. The results for both seasons indicate that there are significantly decreasing trends in the frequency of wet days during the extreme events for most of the stations on the peninsula. However, a smaller number of significant trends was found for extreme intensity.
Identification of the true statistical distributions for various hydrologic data sets is a major problem facing engineers. The four-parameter kappa distribution is a combination of the established distribution including the Generalised Extreme Value (GEV), Generalised Logistic (GL), Generalised Pareto (GP) and the Gumbel distribution were considered in this study. The main objective of this study was to develop the method of LQ-moments for the kappa distribution. The performance of the LQ-moments was compared with L-moments through eight problems using published data sets. The results showed that the performance of both methods, the LQ-moments and L-moments worked equally well.
In most research including environmental research, missing recorded data often exists and has become a common problem for data quality. In this study, several imputation methods that have been designed based on the techniques for functional data analysis are introduced and the capability of the methods for estimating missing values is investigated. Single imputation methods and iterative imputation methods are conducted by means of curve estimation using regression and roughness penalty smoothing approaches. The performance of the methods is compared using a reference data set, the real PM10 data from an air quality monitoring station namely the Petaling Jaya station located at the western part of Peninsular Malaysia. A hundred of the missing data sets that have been generated from a reference data set with six different patterns of missing values are used to investigate the performance of the considered methods. The patterns are simulated according to three percentages (5, 10 and 15) of missing values with respect to two different sizes (3 and 7) of maximum gap lengths (consecutive missing points). By means of the mean absolute error, the index of agreement and the coefficient of determination as the performance indicators, the results have showed that the iterative imputation method using the roughness penalty approach is more flexible and superior to other methods.
This paper presents the accuracy of age statistics in the 1991 census. The quality of age statistics were evaluated using Myers index and United Nations index. The indices obtained were compared to the indices of 1970 and 1980. This study found that age statistics for 1991 census are better than the previous censuses and in general the statistics are having high quality.
Dalam kertas ini dibentangkan ketepatan statistik umur pada banci 1991. Kualiti statistik umur dinilai dengan menggunakan indeks Myers dan United Nations. Indeks yang diperoleh dibandingkan dengan indeks pada banci 1970 dan 1980. Kajian ini mendapati statistik umur banci 1991 lebih baik daripada hasil banci sebelumnya dan pada keseluruhannya ia mempunyai kualiti yang baik.
Sejak taburan normal ditemui dan ianya merupakan salah satu taburan yang penting dalam statistik, terdapat banyak pengujian statistik yang dibangunkan untuk menguji kenormalan data. Namun begitu masih tidak banyak kajian yang dilakukan untuk melihat kembali keupayaan pengujian statistik yang sedia ada. Sebahagian daripada pengujian statistik didapati mudah tetapi hanya sesuai untuk sesuatu keadaan. Dalam kajian ini, pengujian statistik berdasarkan statistik Cramer-von Mises cuba diperbaiki berdasarkan rumus Weibull. Kekuatan statistik yang baru ini dibandingkan kekuatan dengan statistik traditional Anderson-Darling (AD), Cramer von-Mises (CR), Kolmogorov-Smirnov (KS) dan Shapiro-Wilk (SW). Kajian simulasi berdasarkan beberapa taburan yang berbeza menunjukkan pengujian statistik yang dicadangkan paling sesuai untuk menguji kenormalan.
Kajian ini bertujuan mengenal pasti pola taburan kehujanan di Semenanjung Malaysia menggunakan Indeks Kerpasan Piawai bagi skala masa yang berbeza iaitu sebulan, enam bulan dan dua belas bulan. Data kajian adalah data hujan harian dari 75 stesen tadahan hujan yang merangkumi empat zon iaitu Barat Laut, Barat, Barat Daya dan Timur untuk 33 tahun; 1975 – 2007. Hasil kajian mendapati nilai serakan bagi frekuensi keberlakuan keadaan basah/kering bertambah dengan peningkatan skala masa. Kajian pemboleh ubah berkaitan iaitu tempoh, keparahan dan selang ketibaan mendapati wujud peningkatan dalam nilai-nilai maksimum, purata dan sisihan piawai di setiap zon dengan bertambahnya skala masa yang digunakan. Seterusnya, zon Barat Daya secara konsisten mengalami tempoh keadaan basah yang lebih lama berbanding tempoh keadaan kering manakala zon Barat pula menghasilkan nilai sisihan piawai yang paling tinggi berbanding dengan zon lain untuk kesemua pemboleh ubah kajian kecuali intensiti.
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.
This paper offers a technique to create a development index among districts. To determine the weight for each criterion in the index entropy theory was used. Two approaches for criteria normalization were also suggested. The data obtained from 1991 census conducted in Peninsular Malaysia were utilized as illustration.
Kertas ini mencadangkan teknik pembinaan indeks kemajuan daerah. Teori entropy digunakan untuk menentukan pemberat bagi kriteria yang digunakan dalam pembinaan indeks. Dua pendekatan menormalkan data turut dicadangkan. Contoh pembinaan indeks dikemukakan berdasarkan kemudahan asas yang terdapat di daerah-daerah di Semenanjung Malaysia seperti yang diperoleh berdasarkan banci tahun 1991.
Pengecaman senjata api semakin serius dan amat penting di dalam bidang penyiasatan jenayah khususnya untuk tempoh dua dekad ini. Dalam makalah ini, suatu sistem untuk pengecaman senjata api berasaskan tapak kelongsong peluru telah diperkenalkan. Tapak kelongsong peluru adalah satu daripada penunjuk yang amat penting dalam membantu menyelesaikan masalah pengecaman pistol. Peluru yang telah digunakan akan meninggalkan lebih daripada 30 ciri yang amat berharga pada tapak kelongsong bagi membantu pihak tertentu mengecam pistol yang telah diguna. Ciri-ciri tersebut sebagai suatu gabungan membentuk apa yang dikenali sebagai kesan cap jari bagi pistol. Lantaran itu, kajian ini adalah untuk mendapatkan fitur yang sesuai bagi pengecaman senjata api. Terlebih dahulu imej tapak kelongsong peluru ini telah ditemberengkan kepada tiga bahagian, membentuk tiga set imej yang berlainan. Imej-imej ini juga dilakukan prapemprosesan untuk membentuk tiga set imej lagi. Fitur-fitur seterusnya disaring daripada imej asal tapak kelongsong peluru dan imej yang telah melalui prapemprosesan. Dua puluh fitur yang berbeza secara signifikan telah diperoleh dan dikirakan untuk imej-imej asal dan yang telah dilakukan prapemprosesan. Kesemua pemprosesan telah dilakukan menggunakan pengaturcaraan MATLAB. Suatu skim berdasarkan analisis korelasi seterusnya telah diperkenalkan untuk pencarian fitur berdasarkan konsep meminimumkan lewahan data tetapi memastikan ciri-ciri unik tersimpan. Fitur-fitur yang berkorelasi tinggi akan digugurkan pasangannya dan hasilnya tinggal cuma tujuh fitur sahaja. Ketujuh-tujuh fitur ini telah diuji sebagai suatu vektor fitur untuk mengelaskan lima pistol daripada model yang sama menggunakan analisis diskriminan. Hasil pengelasan menunjukkan lebih 80% daripada imej-imej tapak kelongsong peluru itu telah dikelaskan dengan jayanya.