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Fulltext Range-box plotting relating to discrete distribution

Mohd Bakri Adam, Babangida Ibrahim Babura, Kathiresan Gopal

MATEMATIKA, 2018;34(2):187-204.
MyJurnal

The box plot has been used for a very long time since 70s in checking the existence
of outliers and the asymmetrical shape of data. The existing box plot is constructed
using five values of statistics calculated from either the discrete or continous data. Many
improvement of box plots have deviated from the elegant and simplier approach of exploratory
data analysis by incorporating many other statistic values resulting the turning
back of the noble philosophy behind the creation of box plot. The modification using
range value with the minimum and maximum values are being incorporated to suit the
need of selected discrete distribution when outliers is not an important criteria anymore.
The new modification of box plot is not based on the asymmetrical shape of distribution
but more on the spreading and partitioning data into range measure. The new propose
name for the box plot with only three values of statistics is called range-box plot.

Matched MeSH terms: Statistical Distributions
On the estimation of three parameters lognormal distribution based on fuzzy life time data

Shafiq M, Alamgir, Atif M

Sains Malaysiana, 2016;45:1773-1777.

Countless statistical tools are available to extract information from data. Life time modeling is considered as one of
the most prominent fields of statistics, which is evident from the developments made in this field in the last few decades.
Almost every statistic for life time analysis is based on precise life time observations, however, life time is not a precise
measurement but more or less fuzzy. Therefore, in addition to classical statistical tools, fuzzy number approaches to
describe life time data are more suitable. In order to incorporate fuzziness of the observations, fuzzy estimators for the
three parameter lognormal distribution were suggested. The proposed estimators cover stochastic variation as well as
fuzziness of the observations.

Matched MeSH terms: Statistical Distributions
LQ-moments: parameter estimation for kappa distribution

Ani Shabri, Abdul Aziz Jemain

Sains Malaysiana, 2010;39.

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.

Matched MeSH terms: Statistical Distributions
Fulltext An Extended Thickness-Dependent Moisture Absorption Model for Unidirectional Carbon/Epoxy Composites

Azizan A, Johar M, Karam Singh SS, Abdullah S, Koloor SSR, Petrů M, et al.

Polymers (Basel), 2021 Jan 30;13(3).
PMID: 33573112 DOI: 10.3390/polym13030440

Moisture absorption tests for materials that exhibit non-Fickian behavior generally require a relatively long period to reach saturation. Therefore, it would be beneficial to establish a relationship between the moisture content and the thickness to minimize the experimental time and cost. This research characterizes the moisture absorption behavior of AS4/8552 carbon/epoxy composites. Specimens were prepared at 4, 8, and 16 plies and immersed in distilled water at 60 °C. The relationship between the non-Fickian parameters (Fickian to non-Fickian maximum moisture content ratio ϕ, non-Fickian diffusivity per square thickness α, and non-Fickian initiation time to) and thickness was characterized using a thickness-dependent model. A comparison with other materials revealed that all three non-Fickian parameters are able to be fitted using a power law. Nevertheless, the upper boundary for the applicability of this model was not determined in this study. The Weibull distribution plots indicate that the probability of non-Fickian moisture absorption is influenced by ϕ and α at approximately 62% within a normalized thickness range of 2-3. In regards to to, it is 82% at a normalized thickness of 6. Therefore, the Weibull distribution is proposed for the assessment of non-Fickian moisture absorption based on the material's thickness.

Matched MeSH terms: Statistical Distributions
Fulltext Statistical Modelling and Characterization of Experimental mm-Wave Indoor Channels for Future 5G Wireless Communication Networks

Al-Samman AM, Rahman TA, Azmi MH, Hindia MN, Khan I, Hanafi E

PLoS One, 2016 Sep 21;11(9):e0163034.
PMID: 27654703 DOI: 10.1371/journal.pone.0163034

This paper presents an experimental characterization of millimeter-wave (mm-wave) channels in the 6.5 GHz, 10.5 GHz, 15 GHz, 19 GHz, 28 GHz and 38 GHz frequency bands in an indoor corridor environment. More than 4,000 power delay profiles were measured across the bands using an omnidirectional transmitter antenna and a highly directional horn receiver antenna for both co- and cross-polarized antenna configurations. This paper develops a new path-loss model to account for the frequency attenuation with distance, which we term the frequency attenuation (FA) path-loss model and introduce a frequency-dependent attenuation factor. The large-scale path loss was characterized based on both new and well-known path-loss models. A general and less complex method is also proposed to estimate the cross-polarization discrimination (XPD) factor of close-in reference distance with the XPD (CIX) and ABG with the XPD (ABGX) path-loss models to avoid the computational complexity of minimum mean square error (MMSE) approach. Moreover, small-scale parameters such as root mean square (RMS) delay spread, mean excess (MN-EX) delay, dispersion factors and maximum excess (MAX-EX) delay parameters were used to characterize the multipath channel dispersion. Multiple statistical distributions for RMS delay spread were also investigated. The results show that our proposed models are simpler and more physically-based than other well-known models. The path-loss exponents for all studied models are smaller than that of the free-space model by values in the range of 0.1 to 1.4 for all measured frequencies. The RMS delay spread values varied between 0.2 ns and 13.8 ns, and the dispersion factor values were less than 1 for all measured frequencies. The exponential and Weibull probability distribution models best fit the RMS delay spread empirical distribution for all of the measured frequencies in all scenarios.

Matched MeSH terms: Statistical Distributions
Finding the best circular distribution for southwesterly monsoon wind direction in Malaysia

Nur Arina Basilah Kamisan, Abdul Ghapor Hussin, Yong Zulina Zubairi

Sains Malaysiana, 2010;39.

In this paper, four types of circular probability distribution were used to evaluate which circular probability distribution gives the best fitting for southwesterly Malaysian wind direction data, namely circular uniform distribution, von Mises distribution, wrapped-normal distribution and wrapped-Cauchy distribution. The four locations chosen were Alor Setar, Langkawi, Melaka and Senai. Two performance indicators or goodness of fit tests which are mean circular distance and chord length were used to test which distribution give the best fitting.

Matched MeSH terms: Statistical Distributions
A comparative study of extreme rainfall in Peninsular Malaysia: with reference to partial duration and annual extreme series

Wan Zin Wan Zawiah, Abdul Aziz Jemain, Kamarulzaman Ibrahim, Jamaludin Suhaila, Mohd Deni Sayang

Sains Malaysiana, 2009;38.

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.

Matched MeSH terms: Statistical Distributions
Long memory and asymmetric volatility behaviour of the Malaysian stock market: a statistical modelling approach

Abu Hassan Shaari Mohd Nor, Chin WC

Sains Malaysiana, 2006;35:67-73.

This paper analyzes the asymmetric long memory volatility dependency of the interday prices of Composite Index (CI) at Bursa Malaysia by using GARCH family models. The GARCH type models are used with the assumption that the innovations series follow either one of the following distributions: Gaussian, Student -t and skewed Student -t. The stock returns' long memory dependency is determined using the Hurst parameter. The long memory and asymmetric volatility are modelled by fractionally integrated GARCH models. It is found that the asymmetric and long memory GARCH models with skewed student-t distribution give better predictive ability on the volatility of the Kuala Lumpur Composite Index (KLCI).

Matched MeSH terms: Statistical Distributions
Imputing missing values in modelling the PM10 concentrations

Nuradhiathy Abd Razak, Yong Zulina Zubairi, Rossita M. Yunus

Sains Malaysiana, 2014;43:1599-1607.

Missing values have always been a problem in analysis. Most exclude the missing values from the analyses which may lead to biased parameter estimates. Some imputations methods are considered in this paper in which simulation study is conducted to compare three methods of imputation namely mean substitution, hot deck and expectation maximization (EM) imputation. The EM imputation is found to be superior especially when the percentage of missing values is high as it constantly gives low RMSE as compared with other two methods. The EM imputation method is then applied to the PM10 concentrations data set for the southwest and northeast monsoons in Petaling Jaya and Seberang Perai, Malaysia which has missing values. Four types of distributions, namely the Weibull, lognormal, gamma and Gumbel distribution are considered to describe the PM10 concentrations. The Weibull distribution gives the best fit for the southwest monsoon data for Petaling Jaya. The lognormal distribution outperformed the others in describing the southwest monsoon in Seberang Perai. Meanwhile, for the northeast monsoon in both locations, gamma distribution is the best distribution to describe the data.

Matched MeSH terms: Statistical Distributions
The HARX-GJR-GARCH skewed-t multipower realized volatility modelling for S&P 500

Chin WC, Nadira Mohamed Isa, Nadira Mohamed Isa, Lee MC, Poo KH

Sains Malaysiana, 2017;46:107-116.

The heterogeneous autoregressive (HAR) models are used in modeling high frequency multipower realized volatility of the
S&P 500 index. Extended from the standard realized volatility, the multipower realized volatility representations have
the advantage of handling the possible abrupt jumps by smoothing the consecutive volatility. In order to accommodate
clustering volatility and asymmetric of multipower realized volatility, the HAR model is extended by the threshold
autoregressive conditional heteroscedastic (GJR-GARCH) component. In addition, the innovations of the multipower realized
volatility are characterized by the skewed student-t distributions. The extended model provides the best performing insample
and out-of-sample forecast evaluations.

Matched MeSH terms: Statistical Distributions
The extra zeros in traffic accident data: a study on the mixture of discrete distributions

Zamira Hasanah Zamzuri, Mohd Syafiq Sapuan, Kamarulzaman Ibrahim

Sains Malaysiana, 2018;47:1931-1940.

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.

Matched MeSH terms: Statistical Distributions
Fulltext Performance of Variance Targeting Estimator (VTE) under misspecified error distribution assumption

Abdul Rahim, M.A., Zahari, S.M., Shariff, S.S.R.

Pertanika Journal of Science & Technology, 2017;25(2):607-618.
MyJurnal

Parameter estimation in Generalized Autoregressive Conditional Heteroscedastic (GARCH) model has received much attention in the literature. Commonly used quasi maximum likelihood estimator (QMLE) may not be suitable if the model is misspecified. Alternatively, we can consider using variance targeting estimator (VTE) as it seems to be a better fit for misspecified initial parameters. This paper extends the application to see how both QMLE and VTE perform under error distribution misspecifications. Data are simulated under two error distribution conditions: one is to have a true normal error distribution and the other is to have a true student-t error distribution with degree of freedom equals to 3. The error distribution assumption that has been selected for this study are: normal distribution, student-t distribution, skewed normal distribution and skewed student-t. In addition, this study also includes the effect of initial parameter specification.

Matched MeSH terms: Statistical Distributions
Fulltext HAZOP analysis and reliability assessment of closed loop solar water heater system for residential application

Nurul Husna Abd Wahab, Suryani Kamarudin

Journal of Occupational Safety and Health, 2019;16(1):33-44.
MyJurnal

Solar thermal system or solar water heater system is one of the applications used to produce hot water in the residential sector. This paper describes HAZOP analysis and reliability assessment to evaluates the potential hazard and system probability for the closed loop solar thermal system applied for the residential area. Hazard identification for the main system components is analyzed while Fault Tree Analysis (FTA), Reliability Block Diagram (RBD) and Weibull distributions performed to determine the reliability for the overall system. The result shows that there are 49 potential hazards for the system with failure probability at 0.23822 and the reliability is 0.9693. Subsequently, this study determined the potential hazards for the system which can be anticipated by the residential consumer for the safety aspect. Furthermore, the evaluated reliability result shows that the application of closed loop type solar water heater system at residential premises is highly recommended due to its long lasting operational condition.

Matched MeSH terms: Statistical Distributions
Approximate bayesian estimates of weibull parameters with Lindley’s method

Chris Bambey Guure, Noor Akma Ibrahim

Sains Malaysiana, 2014;43:1433-1437.

One of the most important lifetime distributions that is used for modelling and analysing data in clinical, life sciences and engineering is the Weibull distribution. The main objective of this paper was to determine the best estimator for the two-parameter Weibull distribution. The methods under consideration are the frequentist maximum likelihood estimator, least square regression estimator and the Bayesian estimator by using two loss functions, which are squared error and linear exponential. Lindley approximation is used to obtain the Bayes estimates. Comparisons are made through simulation study to determine the performance of these methods. Based on the results obtained from this simulation study the Bayesian approach used in estimating the Weibull parameters under linear exponential loss function is found to be superior as compared to the conventional maximum likelihood and least squared methods.

Matched MeSH terms: Statistical Distributions
Fulltext Utilization of a Mixture Cure Rate Model based on the Generalized Modified Weibull Distribution for the Analysis of Leukemia Patients

Omer ME, Abu Bakar M, Adam M, Mustafa M

Asian Pac J Cancer Prev, 2021 Apr 01;22(4):1045-1053.
PMID: 33906295 DOI: 10.31557/APJCP.2021.22.4.1045

OBJECTIVE: Cure rate models are survival models, commonly applied to model survival data with a cured fraction. In the existence of a cure rate, if the distribution of survival times for susceptible patients is specified, researchers usually prefer cure models to parametric models. Different distributions can be assumed for the survival times, for instance, generalized modified Weibull (GMW), exponentiated Weibull (EW), and log-beta Weibull. The purpose of this study is to select the best distribution for uncured patients' survival times by comparing the mixture cure models based on the GMW distribution and its particular cases.
MATERIALS AND METHODS: A data set of 91 patients with high-risk acute lymphoblastic leukemia (ALL) followed for five years from 1982 to 1987 was chosen for fitting the mixture cure model. We used the maximum likelihood estimation technique via R software 3.6.2 to obtain the estimates for parameters of the proposed model in the existence of cure rate, censored data, and covariates. For the best model choice, the Akaike information criterion (AIC) was implemented.
RESULTS: After comparing different parametric models fitted to the data, including or excluding cure fraction, without covariates, the smallest AIC values were obtained by the EW and the GMW distributions, (953.31/969.35) and (955.84/975.99), respectively. Besides, assuming a mixture cure model based on GMW with covariates, an estimated ratio between cure fractions for allogeneic and autologous bone marrow transplant groups (and its 95% confidence intervals) were 1.42972 (95% CI: 1.18614 - 1.72955).
CONCLUSION: The results of this study reveal that the EW and the GMW distributions are the best choices for the survival times of Leukemia patients.
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Matched MeSH terms: Statistical Distributions
A macroscopic approach to demography

Smith JD

J Math Biol, 2004 Jan;48(1):105-18.
PMID: 14685774

A canonical/lognormal model for human demography is established, specifying the net maternity function and the age distribution for mothers of new-borns using a single macroscopic parameter vector of dimension five. The age distribution of mothers is canonical, while the net maternity function normalizes to a lognormal density. Comparison of an actual population with the model serves to identify anomalies in the population which may be indicative of phase transitions or influences from levels outside the demographic. Tracking the time development of the parameter vector may be used to predict the future state of a population, or to interpolate for data missing from the record. In accordance with classical theoretical considerations of Backman, Prigogine, et al., it emerges that the logarithm of a mother's age is the most fundamental time variable for demographic purposes.

Matched MeSH terms: Statistical Distributions

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