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Research Communicate | 18-March-2020

Alternative approach to moments of order statistics from one-parameter Weibull distribution

The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in

Piyush Kant Rai, Anu Sirohi

Statistics in Transition New Series, Volume 21 , ISSUE 1, 169–178

Research Article | 08-December-2021

Relationships for moments of the progressively Type-II right censored order statistics from the power Lomax distribution and the associated inference

In this paper, we establish several recurrence relations between single and product moments of progressively Type-II right censored order statistics from the power Lomax distribution. The relations enable the computation of all the single and product moments of progressively Type-II right censored order statistics for all sample sizes 𝑛 and all censoring schemes (𝑅1, 𝑅2,…,𝑅𝑚), 𝑚≤𝑛, in a simple recursive manner. The maximum likelihood approach is used for the estimation of the

Jagdish Saran, Narinder Pushkarna, Shikha Sehgal

Statistics in Transition New Series, Volume 22 , ISSUE 4, 191–212

Article | 28-May-2019


The estimation of population parameters might be quite laborious and inefficient, when the sample data have missing values. In comparison follow-up visits, the method of imputation has been found to be a cheaper procedure from a cost point of view. In the present study, we can enhance the performance of imputation procedures by utilizing the raw moments of the auxiliary information rather than their ranks, especially, when the ranking of the auxiliary variable is expensive or difficult to do so

Muhammed Umair Sohail, Javid Shabbir, Farinha Sohil

Statistics in Transition New Series, Volume 20 , ISSUE 1, 21–40

Research Article | 22-January-2018


In this paper, we establish some new recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the Erlangtruncated exponential distribution. These relations generalize those established by Aggarwala and Balakrishnan (1996) for standard exponential distribution. These recurrence relations enable computation of mean, variances and covariances of all progressively Type-II right censored order statistics for all sample sizes in a simple

Mansoor Rashid Malik, Devendra Kumar

Statistics in Transition New Series, Volume 18 , ISSUE 4, 651–668

Article | 20-December-2020

Comparison of selected tests for univariate normality based on measures of moments

Univariate normality tests are typically classified into tests based on empirical distribution, moments, regression and correlation, and other. In this paper, power comparisons of nine normality tests based on measures of moments via the Monte Carlo simulations is extensively examined. The effects on power of the sample size, significance level, and on a number of alternative distributions are investigated. None of the considered tests proved uniformly most powerful for all types of alternative

Czesław Domański, Piotr Szczepocki

Statistics in Transition New Series, Volume 21 , ISSUE 5, 151–178

Article | 27-December-2017


Indian sign language (ISL) is the main communication medium among deaf Indians. An ISL vocabulary show that the hand plays a significant role in ISL. ISL includes static and dynamic hand gesture recognition. The main aim of this paper is to present multi-feature static hand gesture recognition for alphabets and numbers. Here, comparative analysis of various feature descriptors such as chain code, shape matrix, Fourier descriptor, 7 Hu moments, and boundary moments is done. Multi-feature fusion

Gajanan K. Kharate, Archana S. Ghotkar

International Journal on Smart Sensing and Intelligent Systems, Volume 9 , ISSUE 1, 124–147

Article | 03-July-2017


The moments of a random vector based on the definition of the power of a vector, proposed by J. Tatar, are scalar and vector characteristics of a multivariate distribution. Analogously to the univariate case, we distinguish the uncorrected and the central moments of a random vector. Other characteristics of a multivariate distribution, i.e. an index of skewness and kurtosis, have been introduced by using the central moments of a random vector. For the application of the mentioned quantities for

Katarzyna Budny

Statistics in Transition New Series, Volume 18 , ISSUE 1, 1–20

Article | 06-July-2017


derived for the moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, and formulated moments for order statistics. The 𝑇𝐾𝑤 distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of MLEs. The flood data and HIV/ AIDS data applications illustrate the usefulness of the proposed model.

Muhammad Shuaib Khan, Robert King, Irene Lena Hudson

Statistics in Transition New Series, Volume 17 , ISSUE 2, 183–210

Article | 20-September-2020

A New Quasi Sujatha Distribution

The aim of this paper is to introduce a new quasi Sujatha distribution (NQSD), of which the following are particular cases: the Sujatha distribution devised by Shanker (2016 a), the sizebiased Lindley distribution, and the exponential distribution. Its moments and momentsbased measures are derived and discussed. Statistical properties, including the hazard rate and mean residual life functions, stochastic ordering, mean deviations, Bonferroni and Lorenz curves and stress-strength reliability

Rama Shanker, Kamlesh Kumar Shukla

Statistics in Transition New Series, Volume 21 , ISSUE 3, 53–71

Research Article | 27-May-2018


A study on two-parameter power Ishita distribution (PID), of which Ishita distribution introduced by Shanker and Shukla (2017 a) is a special case, has been carried out and its important statistical properties including shapes of the density, moments, skewness and kurtosis measures, hazard rate function, and stochastic ordering have been discussed. The maximum likelihood estimation has been discussed for estimating its parameters. An application of the distribution has been explained with a

Kamlesh Kumar Shukla, Rama Shanker

Statistics in Transition New Series, Volume 19 , ISSUE 1, 135–148

Research Article | 24-August-2017


In this paper a three-parameter weighted Lindley distribution, including Lindley distribution introduced by Lindley (1958), a two-parameter gamma distribution, a two-parameter weighted Lindley distribution introduced by Ghitany et al. (2011) and exponential distribution as special cases, has been suggested for modelling lifetime data from engineering and biomedical sciences. The structural properties of the distribution including moments, coefficient of variation, skewness, kurtosis and index

Rama Shanker, Kamlesh Kumar Shukla, Amarendra Mishra

Statistics in Transition New Series, Volume 18 , ISSUE 2, 291–310

Article | 20-December-2020

The Gamma Kumaraswamy-G family of distributions: theory, inference and applications

In this paper, we introduce a new family of univariate continuous distributions called the Gamma Kumaraswamy-generated family of distributions. Most of its properties are studied in detail, including skewness, kurtosis, analytical comportments of the main functions, moments, stochastic ordering and order statistics. The next part of the paper focuses on a particular member of the family with four parameters, called the gamma Kumaraswamy exponential distribution. Among its advantages, the

Rana Muhammad Imran Arshad, Muhammad Hussain Tahir, Christophe Chesneau, Farrukh Jamal

Statistics in Transition New Series, Volume 21 , ISSUE 5, 17–40

Article | 20-September-2020

Power Size Biased Two-Parameter Akash Distribution

In this paper, the two-parameter Akash distribution is generalized to size-biased twoparameter Akash distribution (SBTPAD). A further modification to SBTPAD is introduced, creating the power size-biased two-parameter Akash distribution (PSBTPAD). Several statistical properties of PSBTPAD distribution are proved. These properties include the following: moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, the maximum likelihood estimation of the distribution

Khaldoon Alhyasat, Ibrahim Kamarulzaman, Amer Ibrahim Al-Omari, Mohd Aftar Abu Bakar

Statistics in Transition New Series, Volume 21 , ISSUE 3, 73–91

Article | 06-July-2017


In this paper a new one-parameter lifetime distribution named “Sujatha Distribution” with an increasing hazard rate for modelling lifetime data has been suggested. Its first four moments about origin and moments about mean have been obtained and expressions for coefficient of variation, skewness, kurtosis and index of dispersion have been given. Various mathematical and statistical properties of the proposed distribution including its hazard rate function, mean residual life function

Rama Shanker

Statistics in Transition New Series, Volume 17 , ISSUE 3, 391–410

Article | 20-September-2020

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments, mean residual life function and Rényi entropy. Three classical procedures for estimating population parameters are analysed. A simulation study is provided to compare the performance of different

Amal S. Hassan, Salwa M. Assar, Ahmed M. Abdelghaffar

Statistics in Transition New Series, Volume 21 , ISSUE 3, 93–107

Research Article | 04-September-2019


In this paper, we have considered the generalized Pareto distribution. Various structural properties of the distribution are derived including (quantile function, explicit expressions for moments, mean deviation, Bonferroni and Lorenz curves and Renyi entropy). We have provided simple explicit expressions and recurrence relations for single and product moments of generalized order statistics from the generalized Pareto distribution. The method of maximum likelihood is adopted for estimating the

Mansoor Rashid Malik, Devendra Kumar

Statistics in Transition New Series, Volume 20 , ISSUE 3, 57–79

Article | 20-September-2020

Generalised Odd Frechet Family of Distributions: Properties and Applications

A new distribution called Generalized Odd Fréchet (GOF) distribution is presented and its properties explored. Some structural properties of the proposed distribution, including the shapes of the hazard rate function, moments, conditional moments, moment generating function, skewness, and kurtosis are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy, and the distribution of order statistics are given. The maximum likelihood estimation technique is used to

Shahdie Marganpoor, Vahid Ranjbar, Morad Alizadeh, Kamel Abdollahnezhad

Statistics in Transition New Series, Volume 21 , ISSUE 3, 109–128

Research Article | 01-June-2020

Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

Abhimanyu Singh Yadav, S. K. Singh, Umesh Singh

Statistics in Transition New Series, Volume 21 , ISSUE 2, 119–141

Article | 20-December-2020

Modelling bid-ask spread conditional distributions using hierarchical correlation reconstruction

, we first normalized marginal distributions so that they were nearly uniform. Then we modelled joint densities as linear combinations of orthonormal polynomials, obtaining their decomposition into mixed moments. Then we modelled each moment of the predicted variable separately as a linear combination of mixed moments of known variables using least squares linear regression. By combining these predicted moments, we obtained the predicted density as a polynomial, for which we can e.g. calculate the

Jarosław Duda, Henryk Gurgul, Robert Syrek

Statistics in Transition New Series, Volume 21 , ISSUE 5, 99–118

Sampling Methods | 22-July-2018


In the present study we have proposed an improved family of estimators for estimation of population mean using the auxiliary information of median, quartile deviation, Gini’s mean difference, Downton’s Method, Probability Weighted Moments and their linear combinations with correlation coefficient and coefficient of variation. The performance of the proposed family of estimators is analysed by mean square error and bias and compared with the existing estimators in the literature. By

Mir Subzar, Showkat Maqbool, Tariq Ahmad Raja, Surya Kant Pal, Prayas Sharma

Statistics in Transition New Series, Volume 19 , ISSUE 2, 219–238

Research Article | 01-June-2020

Beta transmuted Lomax distribution with applications

In this paper we propose and test a composite generalizer of the Lomax distribution .The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Lomax (BTL) distribution. The properties of the distribution are discussed and explicit expressions are derived for the moments, mean deviations, quantiles, distribution of order statistics and reliability. The maximum likelihood method is used for estimating the model parameters, and the finite sample

Ahmed Hurairah, Abdelhakim Alabid

Statistics in Transition New Series, Volume 21 , ISSUE 2, 13–34

Research Article | 13-June-2021

Developing calibration estimators for population mean using robust measures of dispersion under stratified random sampling

In this paper, two modified, design-based calibration ratio-type estimators are presented. The suggested estimators were developed under stratified random sampling using information on an auxiliary variable in the form of robust statistical measures, including Gini’s mean difference, Downton’s method and probability weighted moments. The properties (biases and MSEs) of the proposed estimators are studied up to the terms of first order approximation by means of Taylor’s Series

Ahmed Audu, Rajesh Singh, Supriya Khare

Statistics in Transition New Series, Volume 22 , ISSUE 2, 125–142

Research Article | 27-December-2017


AUV localization is not accurate based on sequence images if moving target is as landmark,so the moving target detection algorithm is studied based on global motion estimation, which detects and eliminates moving target according to the motion inconsistency of the moving target. Generally grid block matching is used in the global motion estimation, it can’t effectively dispose the dynamic background, and the gradient direction invariant moments descriptors method of free circular neighborhood

GAO Jun-chai, LIU Ming-yong, XU Fei

International Journal on Smart Sensing and Intelligent Systems, Volume 7 , ISSUE 1, 360–379

Research Article | 04-September-2019


behaviour and pattern, first four moments i.e., mean, variance, skewness and kurtosis are derive and compared with the sum of binomial simple random samples with same success probability. The proposed procedure has been illustrated through a reallife data on survivorship of children below one year in Empowered Action Groups (EAG) states of India.

Vivek Verma, Dilip C. Nath

Statistics in Transition New Series, Volume 20 , ISSUE 3, 1–29

Article | 15-March-2019


In this study, we introduce a new model called the Extended Exponentiated Power Lindley distribution which extends the Lindley distribution and has increasing, bathtub and upside down shapes for the hazard rate function. It also includes the power Lindley distribution as a special case. Several statistical properties of the distribution are explored, such as the density, hazard rate, survival, quantile functions, and moments. Estimation using the maximum likelihood method and inference on a

V. Ranjbar, M. Alizadeh, G. G. Hademani

Statistics in Transition New Series, Volume 19 , ISSUE 4, 621–643

Article | 20-December-2020

A new generalization of the Pareto distribution and its applications

This paper introduces a new generalization of the Pareto distribution using the MarshallOlkin generator and the method of alpha power transformation. This new model has several desirable properties appropriate for modelling right skewed data. The Authors demonstrate how the hazard rate function and moments are obtained. Moreover, an estimation for the new model parameters is provided, through the application of the maximum likelihood and maximum product spacings methods, as well as the Bayesian

Ehab M. Almetwally, Hanan A. Haj Ahmad

Statistics in Transition New Series, Volume 21 , ISSUE 5, 61–84

Research Article | 06-July-2018

“If you talk, you are just talking. If I talk is that bragging?” Perspectives of Parents with Young Gifted Children in New Zealand.

rich picture of the experiences and perspectives of these parents. Although parents shared both joyful and painful moments of parenting, key findings included three particular areas of concern for parents: a) concern over misunderstanding and negativity; b) parents’ concern with gifted children’s intense behaviour; and c) parents’ concern with gifted children’s educational experiences. In response to these concerns, parents took on the role of advocates for their gifted

Lakshmi Chellapan, Valerie Margrain

Apex, Volume 18 , ISSUE 1, 10–24

research-article | 30-November-2020


for RC columns. The RC columns can be designed by calculating axial force and moment values from the interaction diagram. The interaction diagrams are usual tools for RC cross-section analysis and design. The interaction diagrams are plotted to use the ultimate values of the bending moments and axial force for evaluating the cross-section strength [23, 24]. The interaction diagrams present a widely used practical tool for the design of RC structures, which is selected for a few reasons including

Abdulkadir Cüneyt AYDIN, Mahmut KILIÇ, Mahyar MAALI, Barış BAYRAK, Erkan TUNÇ

Architecture, Civil Engineering, Environment, Volume 14 , ISSUE 2, 47–65

Research Article | 18-March-2020

Parametric prediction of finite population total under Informative sampling and nonignorable nonresponse

the dependence of the probability of nonresponse on unobserved or missing observations. The main aim of the paper is to consider how to account for the joint effects of informative sampling designs and notmissing-at-random response mechanism in statistical models for complex survey data. For this purpose, theoretically, we use the response distribution and relationships between the moments of the superpopoulation, the sample, sample-complement, response, and nonresponse distributions for the

Abdulhakeem Eideh

Statistics in Transition New Series, Volume 21 , ISSUE 1, 13–35

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