Fahimah Al-Awadhi

Marshall–Olkin Extended Lomax Distribution and Its Application to Censored Data

This paper investigates properties of a new parametric distribution generated by Marshall and Olkin (1997) extended family of distributions based on the Lomax model. We show that the proposed distribution can be expressed as a compound distribution with mixing exponential model. Simple sufficient conditions for the shape behavior of the density and hazard rate functions are given. The limiting distributions of the sample extremes are shown to be of the exponential and Fréchet type. Finally, utilizing maximum likelihood estimation, the proposed distribution is fitted to randomly censored data.

Bayes two-sample prediction of generalized order statistics with fixed and random sample size

Abstract Bayes two-sample point and interval predictors of generalized order statistics are obtained when the future sample size is fixed and when it is random. A general distribution is considered for each of the underlying population and the prior. Illustrative examples are given in which the underlying population distributions are specialized to Burr type XII and Weibull models. Numerical computations have been carried out for predictions of future ordinary order statistics and ordinary records.

Three-dimensional Bayesian image analysis and confocal microscopy

We report methods for tackling a challenging three-dimensional (3D) deconvolution problem arising in confocal microscopy. We fit a marked point process model for the set of cells in the sample using Bayesian methods; this produces automatic or semi-automatic segmentations showing the shape, size, orientation and spatial arrangement of objects in a sample. Importantly, the methods also provide measures of uncertainty about size and shape attributes. The 3D problem is considerably more demanding computationally than the two-dimensional analogue considered in Al-Awadhi et al. [2] due to the much larger data set and higher-dimensional descriptors for objects in the image. In using Markov chain Monte Carlo simulation to draw samples from the posterior distribution, substantial computing effort can be consumed simply in reaching the main area of support of the posterior distribution. For more effective use of computation time, we use morphological techniques to help construct an initial typical image under the posterior distribution.

Commute times and the effective resistances of random trees

In this article we study the commute and hitting times of simple random walks on spherically symmetric random trees in which every vertex of level n has outdegree 1 with probability 1−qn and outdegree 2 with probability qn. Our argument relies on the link between the commute times and the effective resistances of the associated electric networks when 1 unit of resistance is assigned to each edge of the tree.

Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian kriged Kalman model

This article describes the hierarchical Bayesian approach for predicting average hourly concentrations of ambient non-methane hydrocarbons (NMHC) in Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to predict the concentration level of NMHC in unmonitored areas. Here an attempt is made for the prediction of unmeasured concentration of NMHC at two additional locations in Kuwait. We will implement a kriged Kalman filter (KKF) hierarchical Bayesian approach assuming a Gaussian random field, a technique that allows the pooling of data from different sites in order to predict the exposure of the NMHC in different regions of Kuwait. In order to increase the accuracy of the KKF we will use other statistical models such as imputation, regression, principal components, and time series analysis in our approach. We considered four different types of imputation techniques to address the missing data. At the primary level, the logarithmic field is modeled as a trend plus Gaussian stochastic residual model. The trend model depends on hourly meteorological predictors which are common to all sites. The residuals are then modeled using KKF, and the prediction equation is derived conditioned on adjoining hours. On this basis we developed a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales, we can impute Kuwait’s hourly non-methane hydrocarbons field.

A multivariate prediction of spatial process with non-stationary covariance for Kuwait non-methane hydrocarbons levels

Predicting unmeasured realizations of multivariate spatial process responses is a fundamental problem in environmetrics. The study of levels of air pollutants is important for understanding and improving air quality in major urban areas. This research aims to handle the prediction in a Bayesian framework for non-methane hydrocarbons NMHC pollutant for the State of Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to study the distribution level of NMHC with respect to time and metreological parameters and space and use this distribution to predict the concentration of NMHC in other sites of Kuwait using the minimum amount of data (reducing the cost). We will implement a hierarchical Bayesian approach assuming Gaussian random field technique that allows us to pool the data from different sites in predicting the exposure of the non-methane hydrocarbons in different regions of Kuwait.

Marshall–Olkin extended two-parameter bathtub-shaped lifetime distribution

ABSTRACT The Marshall–Olkin extended two-parameter bathtub distribution is introduced and its structural properties are investigated, including the compounding representation of the distribution, the shapes of the density and the hazard rate function, the moments and quantiles. Estimation of the model parameters by maximum likelihood is discussed. Applications to some real data sets which motivate the usefulness of the model are provided. Comparison between the proposed model and other commonly used distributions is performed using real data sets. A simulation study is presented to investigate the accuracy of the estimates of the models parameters.

Bayesian change points analysis for earthquakes body wave magnitude

ABSTRACT Recently, the world has experienced an increased number of major earthquakes. The Zagros belt is among the most seismically active mountain ranges in the world. Due to Kuwaits location in the southwest of the Zagros belt, it is affected by relative tectonic movements in the neighboring region. It is vital to assess the Zagros seismic risks in Kuwait using recent data and coordinate with the competent authorities to reduce those risks. Using the body wave magnitude (Mb) data collected in Kuwait, we want to assess the recent changes in the magnitude of earthquakes and its variations in Kuwaits vicinity. We built a change point model to detect the significant changes in its parameters. This paper applies a hierarchical Bayesian technique and derives the marginal posterior density function for the Mb. Our interest lies in identifying a shift in the mean of a single or multiple change points as well as the changes in the variation. Building upon the model and its parameters for the 2002–2003 data, we detected three change points. The first, second and third change points occurred in September 2002, April 2003 and August 2003, respectively.

The speed of random walks on trees and electric networks

The speed of the random walk on a tree is the rate of escaping its starting point. It depends on the way that the branching occurs in the sense that if the average number of branching is large, the speed is more likely to be positive. The speed on some models of random trees is calculated via calculating the hitting times of the consecutive levels of the tree.

Spatial–temporal interpolation of non methane hydrocarbon levels in Kuwait

ABSTRACT This article handles the prediction of hourly concentrations ofnon methane hydrocarbon (NMHC) pollutants at 15 unmonitored sites in Kuwait using the data recorded from 6 monitored stations at successive time points. The trend model depends on hourly meteorological variables and seasonal effects. The stochasticcomponent of the trend model which has spatiotemporal features is modeled as autoregressive temporal process. A spatial predictive distribution for residuals of the AR model is developed for the unmonitored sites. By transforming the predicted residuals back to the original data scales, we impute Kuwait’s hourly NMHC field.