scholarly journals The recurrence relations of order statistics moments for power Lomax distribution

2018 ◽  
Vol 52 (1) ◽  
pp. 75-90
Author(s):  
DEVENDRA KUMAR ◽  
SANKU DEY ◽  
MAZEN NASSAR ◽  
PREETI YADAV
Keyword(s):  
Bladder Cancer ◽  
Order Statistics ◽  
Recurrence Relations ◽  
Sample Sizes ◽  
Double Product ◽  
Cancer Data ◽  
Lomax Distribution ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides better fits for bladder cancer data (Lee and Wang, 2003) than the Lomax, exponential Lo- max, Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit expressions as well as recurrence relations for the single and double (product) moments have been derived from the power Lomax distribution. These recurrence relations enable computation of the mean, variance, skewness and kurtosis of all order statistics for all sample sizes in a simple and efficient manner. By using these relation, the mean, variance, skewness and kurtosis of order statistics for sample sizes up to 5 for various values of shape and scale parameters are tabulated. Finally, remission times (in months) of bladder cancer patients have been analyzed to show how the proposed relations work in practice.

scholarly journals Exact Moments of order Statistics from The exponentiated Lomax distribution

2016 ◽  
Vol 12 (3) ◽  
pp. 6074-6086
Author(s):  
Nasr Ibrahim Rashwan
Keyword(s):  
Probability Density Function ◽  
Order Statistics ◽  
Recurrence Relations ◽  
Exact Form ◽  
Single Product ◽  
Lomax Distribution ◽  
Percentage Points ◽  
Moments Of Order Statistics ◽  
Single And Product Moments ◽  
Skewness And Kurtosis

In this paper, order statistics from the exponentiated Lomax distribution (ELD) are obtained. Exact form for the single, product and Triple moment of order statistics from ELD are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic are presented. Some recurrence relations for the single and product moments of order statistics from ELD are established. Also, the percentage points of single order statistics from ELD are computed.

scholarly journals Abnormal Portfolio Asset Allocation Model: Review

2020 ◽  
Vol 1 (1) ◽  
pp. 46-54
Author(s):  
Nurfadhlina Bt Abdul Halima ◽  
Dwi Susanti ◽  
Alit Kartiwa ◽  
Endang Soeryana Hasbullah
Keyword(s):  
Asset Allocation ◽  
Asset Returns ◽  
Higher Moments ◽  
Investment Portfolio ◽  
Allocation Model ◽  
Model Review ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis ◽  
Normally Distributed

It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.

scholarly journals Expectation Properties of Generalized Order Statistics from Poisson Lomax Distribution

2020 ◽  
Vol 9 (3) ◽  
pp. 735-747
Author(s):  
Haseeb Athar ◽  
Zubdahe Noor ◽  
Saima Zarrin ◽  
Hanadi N.S. Almutairi
Keyword(s):  
Order Statistics ◽  
Recurrence Relations ◽  
Generalized Order Statistics ◽  
Lifetime Data ◽  
Product Moments ◽  
Lomax Distribution ◽  
Single And Product Moments ◽  
Generalized Order

The Poisson Lomax distribution was proposed by [3], as a useful model for analyzing lifetime data. In this paper,we have derived recurrence relations for single and product moments of generalized order statistics for this distribution. Further, characterization of the distribution is carried out. Some deductions and particular cases are also discussed.

scholarly journals A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data

2019 ◽  
pp. 1-17
Author(s):  
Peter O. Koleoso ◽  
Angela U. Chukwu
Keyword(s):  
Bladder Cancer ◽  
Maximum Likelihood ◽  
Order Statistics ◽  
Hazard Function ◽  
Probability Distributions ◽  
Survival Function ◽  
Statistical Properties ◽  
Cancer Data ◽  
Method Of Maximum Likelihood ◽  
Flexible Model

The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.

scholarly journals Progressively Type-II Right Censored Order Statistics from Hjorth Distribution and Related Inference

2020 ◽  
Vol 8 (2) ◽  
pp. 481-498
Author(s):  
NARINDER PUSHKARNA ◽  
JAGDISH SARAN ◽  
KANIKA VERMA
Keyword(s):  
Order Statistics ◽  
Recurrence Relations ◽  
Type Ii ◽  
Sample Sizes ◽  
Product Moments ◽  
Scale Parameters ◽  
Censored Samples ◽  
Progressive Type ◽  
Right Censored Order Statistics ◽  
Single And Product Moments

In this paper some recurrence relations satisfied by single and product moments of progressive Type-II right censored order statistics from Hjorth distribution have been obtained. Then we use these results to compute the moments for all sample sizes and all censoring schemes (R1,R2,...,Rm),m ≤ n, which allow us to obtain BLUEs of location and scale parameters based on progressive type-II right censored samples.

scholarly journals The power Lomax distribution with an application to bladder cancer data

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
El-Houssainy A. Rady ◽  
W. A. Hassanein ◽  
T. A. Elhaddad
Keyword(s):  
Bladder Cancer ◽  
Cancer Data ◽  
Lomax Distribution

scholarly journals On estimating the shape and dynamics of phenotypic distributions in ecology and evolution

2021 ◽  
Author(s):  
Brian Maitner ◽  
Aud Halbritter ◽  
Richard Telford ◽  
Tanya Strydom ◽  
Julia Chacon-Labella ◽  
...  
Keyword(s):  
Intraspecific Variation ◽  
Evolutionary Biology ◽  
R Package ◽  
Sampling Unit ◽  
Weighted Mean ◽  
Central Moments ◽  
Community Weighted Mean ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis

Estimating the distribution of phenotypes in populations and communities is central to many questions in ecology and evolutionary biology. These distributions can be characterized by their moments: the mean, variance, skewness, and kurtosis. Typically, these moments are calculated using a community-weighted approach (e.g. community-weighted mean) which ignores intraspecific variation. As an alternative, bootstrapping approaches can incorporate intraspecific variation to improve estimates, and also quantify uncertainty in the estimate. Here, we compare the performance of different approaches for estimating the moments of trait distributions across a variety of sampling scenarios, taxa, and datasets. We introduce the traitstrap R package to facilitate inferences of trait distributions via bootstrapping. Our results suggest that randomly sampling ~9 individuals per sampling unit and species, focusing on covering all species in the community, and analysing the data using nonparametric bootstrapping generally enables reliable inference on trait distributions, including the central moments, of communities.

scholarly journals Power generalized Weibull distribution based on order statistics

2017 ◽  
Vol 51 (1) ◽  
pp. 61-78 ◽  
Author(s):  
DEVENDRA KUMAR ◽  
SANKU DEY
Keyword(s):  
Weibull Distribution ◽  
Order Statistics ◽  
Recurrence Relations ◽  
Sample Sizes ◽  
Efficient Manner ◽  
Product Moments ◽  
Scale Parameters ◽  
Moments Of Order Statistics ◽  
Single And Product Moments

In this article, we establish recurrence relations for the single and product moments of order statistics from the power generalized Weibull (PGW) distribution due to Bagdonovacius and Nikulin (2002). These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we have obtained the means, variances and covariances of order statistics from samples of sizes up to 5 for various values of the shape and scale parameters and present them in figures.

scholarly journals Divergent Abiotic Stressors Drive Grassland Community Assembly of Tibet and Mongolia Plateau

2022 ◽  
Vol 12 ◽  
Author(s):  
Jianming Wang ◽  
Mingxu Li ◽  
Li Xu ◽  
Congcong Liu ◽  
Pu Yan ◽  
...  
Keyword(s):  
Community Assembly ◽  
Future Climate Change ◽  
Dry Matter Content ◽  
Grassland Community ◽  
Plant Trait ◽  
Abiotic Stressors ◽  
Trait Convergence ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis

Multiple ecological processes simultaneously govern community assembly, but it remains unclear how abiotic stressors regulate the relative importance of these processes among different biogeographic regions. Therefore, we conducted a comprehensive study on the responses of community assembly to varying environmental gradients, using the mean, variance, skewness, and kurtosis of plant height (height), specific leaf area (SLA) and leaf dry matter content (LDMC) distributions on the Tibetan Plateau (TP) and the Mongolian Plateau (MP). Our results showed that the prevalence of trait convergence across all grasslands in both TP and MP seem to be the result of abiotic filtering or weaker competitive exclusion etc. These trait-convergence assembly processes decrease the functional dispersion but increase the evenness of the trait frequency distribution. The mean, variance, skewness, and kurtosis responses of grassland communities to abiotic stress varied between the TP and MP. On average, plant trait distribution was mainly driven by temperature on the TP, and low-temperature stress altered the community assembly rules. In contrast, water availability shaped plant trait frequency distributions on the MP, and drought stress mediated the balance between different assembly processes. Our results provide empirical evidence that divergent abiotic stressors regulate the grassland community assembly on the TP and MP. Together, our study speculates that different aspects of future climate change, such as climate warming and changing precipitation patterns, on community assembly are dependent on regional climatic regimes.

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