N. F. Abdo

Bio: N. F. Abdo is an academic researcher. The author has contributed to research in topics: Gompertz–Makeham law of mortality & Quantile. The author has an hindex of 3, co-authored 3 publications receiving 66 citations.

Exponential Lomax Distribution

Abstract: In this paper, A new distribution called Exponential Lomax distribution is introduced It is seemed that the parameter values of our new distribution are depending on decreasing and upside-down bathtub failure rate function Also, the statistical properties of this model are studied, such as, quantiles, moments, mean deviation Moreover, maximum likelihood estimators of its parameters are discussed Finally, the procedure is illustrated by real data set It is shown that the introduced model is more competitive than other models

Reliability Properties of Seven Parameters Burr XII Distribution

Abstract: This paper investigates reliability properties of a flexible extended (seven parameters) Burr XII family of distributions. Moreover, closed forms for n-th moments are derived.

Reliability Properties of Extended Makeham Distributions

Abstract: The Makeham distribution describes the age dynamics of human mortality rather accurately in the age window of about 30-80 years. At more advanced ages the death rates do not increase as fast as predicted by this mortality law – a phenomenon known as the late-life mortality deceleration. Historical decline in human mortality before 1950s was mostly due to the decrease in the age-independent mortality component (Makeham parameter), while the agedependent mortality component was surprisingly stable in history before 1950s. After that a new mortality trend has started, leading to unexpected decline in mortality rates at advanced ages and “de-rectangularization” of the survival curve.

Extreme Value Theory

Abstract: Extreme Value Theory is the branch of statistics that is used to model extreme events. The topic is of interest to meteorologists because much of the recent literature on climate change has focussed on the possibility that extreme events (very high or low temperatures, high precipitation events, droughts, hurricanes etc.) may be changing in parallel with global warming. As a specific example, the paper by Stott, Stone and Allen (2004) used the generalized Pareto distribution (see Section 2) to estimate the probability of the European heatwave event of 2003 under two conditions, (a) based on climate model data without an anthropogenic signal, (b) including anthropogenic effects (greenhouse gases etc.). They estimated a probability of about 1/1000 under (a) but about 1/250 under (b). Although even the probability under (b) is low, the increase in probability compared with (a) led them to conclude that the fraction of attributable risk due to the anthropogenic influence is about 75%. Another example of the use of statistics to examine trends in probabilities of extreme events is the recent paper by Elsner et al. (2008), which is highly relevant to the question of whether there is an increasing trend in severe hurricanes that may possibly be associated with anthropogenic global warming.

Parameter induction in continuous univariate distributions: Well-established G families

Abstract: The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy-generalized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.

The power Lomax distribution with an application to bladder cancer data.

Abstract: A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution.

A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

Abstract: Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

Weighted Lomax distribution

Abstract: The Lomax distribution (Pareto Type-II) is widely applicable in reliability and life testing problems in engineering as well as in survival analysis as an alternative distribution. In this paper, Weighted Lomax distribution is proposed and studied. The density function and its behavior, moments, hazard and survival functions, mean residual life and reversed failure rate, extreme values distributions and order statistics are derived and studied. The parameters of this distribution are estimated by the method of moments and the maximum likelihood estimation method and the observed information matrix is derived. Moreover, simulation schemes are derived. Finally, an application of the model to a real data set is presented and compared with some other well-known distributions.