Papers by Anwar H Joarder
BL College Journal, Nov 30, 2022
We review important probability issues in sampling from simple random sampling without replacemen... more We review important probability issues in sampling from simple random sampling without replacement. The inclusion probability can be calculated by enumerating samples which is formidable for most cases of large samples or large population. A good number of possible situations have been considered. We prove that hypergeometric mass function provides an elegant solution to the problem.
BL College Journal, Jun 30, 2022
The joint distribution of correlated sample variances and their product moments have been derived... more The joint distribution of correlated sample variances and their product moments have been derived. Finite expressions have been derived for product moments of sample variances of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution of a sample variance given the other variance have also been discussed. Shannon entropy of the distribution is also derived. When the variables are uncorrelated, the resulting characteristics match with the independent case of sample variances.
Revista Colombiana de Estadistica, Dec 1, 2013
The distribution of the linear combination of two chi-square variables is known if the variables ... more The distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficients of skewness and kurtosis are derived. Results match with the independent case when the variables are uncorrelated. The graph of the density function is presented.
Metrika, 1998
In this paper, a family of estimators for the finite population variance investigated by Srivasta... more In this paper, a family of estimators for the finite population variance investigated by Srivastava and Jhajj (1980) is studied under two different situations of random non-response considered by Tracy and Osahan (1994). Asymptotic expressions for the biases and mean squared errors of members of the proposed family are obtained; in addition, an asymptotic optimum estimator(AOE) is also identified. Estimators suggested by Singh and Joarder (1998) are shown to be members of the proposed family. A correction to the Singh and Joarder (1998) results is also presented.
International Journal of Heat and Mass Transfer, 2015
In this paper unsteady magnetohydrodynamic convection has been analyzed using numerical and stati... more In this paper unsteady magnetohydrodynamic convection has been analyzed using numerical and statistical techniques for a semicircular-shaped enclosure filled with ferrofluid. Cobalt-kerosene ferrofluid is considered for the present investigation. Galerkin weighted residuals method of finite element ananlysis is adopted for the numerical simulation. The effects of Rayleigh number (Ra), solid volume fraction (/) of ferrofluid and Hartmann number (Ha) are considered as pertinent parameters and varied for a wide range of values (Ra = 10 5-10 7 , / = 0-0.15, Ha = 0-50) to capture the flow and thermal interaction phenomena for unsteady situation. It is observed that higher ferrofluid solid volume fraction escalates the heat transfer rate. Enhancing the intensity of external magnetic field (by increasing Ha) retards the heat transfer rate while increment of Ra exhibits improvement on the heat transfer. It is also found that there exists a strong interacion between ferromagnetic particle (cobalt) and base fluid (kerosene) in the presence of magnetic field which can be utilized properly for desired heat transfer augmentation. If / = 0 (or / = 0.15) and Ra is changed from 10 5 to 10 7 , the linear dependence of W max on time changes significantly from positive to negative.
The Multivariate T-Distribution and Its Applications in Regression Analysis
Analytical Production Modeling for Hydraulically Fractured Gas Reservoirs
Petroleum Science and Technology, Jun 20, 2007
Unsteady analysis of natural convection in a carbon nanotube-water filled cavity with an inclined heater
Numerical Heat Transfer Part A-applications, Jan 21, 2016
ABSTRACT A finite element solution has been performed in this work to solve unsteady governing eq... more ABSTRACT A finite element solution has been performed in this work to solve unsteady governing equations of natural convection in a carbon nanotube–water-filled cavity with inclined heater. The temperature of ceiling and left vertical walls is lower than that of the heater while the other walls are adiabatic. The main governing parameters are nanofluid volume fraction and Rayleigh number (Ra). It is found that the heat transfer rate shows different trends based on Rayleigh number and it increases with increase in nanoparticle volume fraction. It has been estimated that average Nusselt number (Nu) is dependent onRa through power regression models with strong positive linear correlation between ln (Nu) and ln (Ra). In particular, for the maximum time, when the solid volume fraction is varied from 0 to 0.1 the dependence between average Nu and linear Ra, on a logarithmic scale, is very high.
WSEAS TRANSACTIONS ON MATHEMATICS, 2020
Moments of multivariate Wishart Distribution are known up to fourth order. But in many contexts, ... more Moments of multivariate Wishart Distribution are known up to fourth order. But in many contexts, moments of some functions of Wishart distribution and Inverted Wishart Distribution have been found useful in risk theoretic estimation of covariance matrix and its characteristics. In this paper we review moments of some important functions of Wishart and Inverted Distributions.
This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
On the Exact Distribution of the Difference Between Two Chi-Square Variables
Bulletin of the Malaysian Mathematical Sciences Society
CLASSROOM NOTE An algorithm for sample variance
Alternative Ways for the Covariance Between Sample Mean and Variance
Bulletin of the Malaysian Mathematical Sciences Society
The regression line simplified
Ganit: Journal of Bangladesh Mathematical Society,, 2021
It is not popularly realized that the factorization of a general quadratic expression basically r... more It is not popularly realized that the factorization of a general quadratic expression basically requires solution to a hyperbola and a line. This fact is conspicuously pointed out and a few solutions to the problem are demonstrated that are scattered in the literature. In the high school level, the coefficients of a quadratic expression are mostly integers, and factorization is performed by the popular method of decomposition of the middle term. In this expository note, we have presented it in a simpler way that shows both insight and reasoning into the problem. Some other methods, namely, Linear Method, Average Method and Difference of two Squares Method are also discussed. Depending on the background, a reader may prefer a particular method to the others. The expository nature and artistry in presentation of the paper are expected to make the learning of the topic amusing and instructive.
GANIT: Journal of Bangladesh Mathematical Society, 2021
It is not popularly realized that the factorization of a general quadratic expression basically r... more It is not popularly realized that the factorization of a general quadratic expression basically requires solution to a hyperbola and a line. This fact is conspicuously pointed out and a few solutions to the problem are demonstrated that are scattered in the literature. In the high school level, the coefficients of a quadratic expression are mostly integers, and factorization is performed by the popular method of decomposition of the middle term. In this expository note, we have presented it in a simpler way that shows both insight and reasoning into the problem. Some other methods, namely, Linear Method, Average Method and Difference of two Squares Method are also discussed. Depending on the background, a reader may prefer a particular method to the others. The expository nature and artistry in presentation of the paper are expected to make the learning of the topic amusing and instructive. GANITJ. Bangladesh Math. Soc.41.1 (2021) 15-25
Australian senior mathematics journal, 2015
An algorithm is presented for factorising a quadratic expression to facilitate instruction and le... more An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers.
An attempt is made to put the notion of sample quartiles on a mathematical footing in the light o... more An attempt is made to put the notion of sample quartiles on a mathematical footing in the light of ranks of observations, and equisegmentation property that the number of ranks below that of the first quartile, that between the consecutive quartiles, and that above the third quartile are the same. Ranks of sample quartiles provided by the proposed Halving Method, based on hinges, does satisfy the property. 1.
A method called the Remainder Method is proposed for the calculation of sample quantiles of a giv... more A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. We propose the criterion of equisegmentation property that the number of observations below the first quantile, that between the consecutive quantiles, and that above the last quantile are the same. The formulae for quantiles offered by the proposed method satisfy the equisegmentation property, and more interestingly provide the number of quantiles having integer ranks. Some open problems are indicated.
Panamerican Mathematical Journal, 2013
The generalized mixture of standard normal distribution and skew normal distributions (GMNSN) has... more The generalized mixture of standard normal distribution and skew normal distributions (GMNSN) has been studied by Kumar and Anusree. Several properties such as the characteristic function, mean, variance, coe¢ cient of skewness, etc were obtained. In this paper, we investigate this mixture model by providing the same properties and some additional properties using more well-known special functions and simpler moment expressions.
Uploads
Papers by Anwar H Joarder