Hasil untuk "Probabilities. Mathematical statistics"

F. P. Ramsey

S.M. Sunoj , N. Unnikrishnan Nair

In the present work we propose survival copula entropy as an alternative to Shannon entropy, cumulative residual entropy and copula entropy measures in computing the uncertainty in bivariate populations. We examine the relationships between the various measures. The properties of survival copula entropy are discussed, especially its applications to ascertain the nature and extent of uncertainty among copulas.

Mohd Fazril Izhar Mohd Idris, Khairu Azlan Abd Aziz, Ardini Athirah Mhd Munawar

Investment decisions are essential for achieving financial growth and stability. Young Malaysians, however, often face challenges such as limited financial resources, rising living costs, and low financial literacy. Common investment options in Malaysia include gold, stocks, property, and cryptocurrency. Each option differs in capital requirements, profitability, risk level, and long-term viability. Selecting the most appropriate investment is difficult because decision making is often subjective and influenced by uncertainty. Conventional multi criteria decision making (MCDM) methods such as Simple Additive Weighting (SAW), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and Analytic Hierarchy Process (AHP) have been widely used, but they are less effective in dealing with this challenge. To overcome this limitation, this study applies the Fuzzy Analytic Hierarchy Process (FAHP), which integrates fuzzy logic with AHP to capture expert evaluations more realistically. Four investment alternatives are assessed based on capital, profit, risk, and sustainability. The results indicate that gold is the most preferred investment option, followed by property, stocks, and cryptocurrency. By applying FAHP to investment decision-making in Malaysia, this study introduces a novel framework that not only supports young investors in making strategic choices but also offers insights that may inform financial literacy programs and policy initiatives under uncertain market conditions.

Abdiel Bellamy Thomas, Nikken Prima Puspita, Fitriani Fitriani

Research on ring derivation is one of the studies that is quite popular among algebra lovers. The definition of the derivation on the ring is motivated by the derivation in calculus which has Leibniz's rule. The purpose of this paper is to show some of the derivation properties on several rings, namely divisor rings, cartesian product rings, and factor rings. Let be a commutative ring with multiplicative identity and A the set of multiplicative closed that has non-zero divisor. In this paper, we have shown some results of derivation on ring theory. If is a ring derivation of R and is a divisor ring of , we can construct for all , then the map is a derivation on . The concept of embedding one ring into another ring can be used so that the ring of constant of , namely , is a subring of the divisor ring . Related to the ideal on ring theory, if I is an ideal of R, then where is also a derivation on the ring . The last result in this paper comes from the ring of cartesian product, take be a ring with derivation for . The cartesian product ring have a derivation ring defined by for any .

Putu Krishnanda Supriyatna, Dedy Dwi Prastyo, Muhammad Sjahid Akbar

Economic growth is crucial for planning, yet delayed data releases challenge timely decision-making. Nowcasting offers near-real-time insights using high-frequency indicators (released monthly, weekly, or even daily) to predict low-frequency variables (quarterly or yearly). This study uses high-frequency indicators (monthly), such as stock price changes, air quality, transportation data, financial conditions, and Google Trends, to nowcast quarterly GDP through the Dynamic Factor Model (DFM). The data used span from January 2010 until March 2023, which is split into two: January 2010 until March 2022 for training data and the rest as testing data. Compared to the benchmark Autoregressive Moving Average with Exogenous Variables (ARMAX) model, DFM demonstrates superior accuracy with lower symmetric Mean Absolute Percentage Error (sMAPE). In addition, to evaluate the model performance in nowcasting the GDP across the sector using DFM, the additional metrics, i.e., Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD), and Adjusted R-squared, concluded that in the industrial and transportation sectors results in sufficient nowcasting of GDP, Meanwhile, In the financial sector, the results of the nowcasting GDP give poor estimation results that need improvement.

F. Llorente, Luca Martino, D. Delgado et al.

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.

J. Lasserre, Edouard Pauwels, M. Putinar

The Christoffel–Darboux kernel, a central object in approximation theory, is shown to have many potential uses in modern data analysis, including applications in machine learning. This is the first book to offer a rapid introduction to the subject, illustrating the surprising effectiveness of a simple tool. Bridging the gap between classical mathematics and current evolving research, the authors present the topic in detail and follow a heuristic, example-based approach, assuming only a basic background in functional analysis, probability and some elementary notions of algebraic geometry. They cover new results in both pure and applied mathematics and introduce techniques that have a wide range of potential impacts on modern quantitative and qualitative science. Comprehensive notes provide historical background, discuss advanced concepts and give detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering or economics will find new perspectives on traditional themes, along with challenging open problems.

M. Khalifa Saad, R. A. Abdel-Baky

Curves on surfaces and their frames play an important role in differential geometry and in many branches of science such as mechanics and physics. So, we are interested in studying one of these surfaces along a curve lying on a surface. In this paper, we define a surface normal to a surface along a curve lying on a surface in Euclidean 3-space E3. Then, we analyze the necessary and sufficient conditions for that surface to be a ruled surface. Finally, we illustrate the convenience and efficiency of this approach with some representative examples.

سلوى صلاح الدين, بشار الطالب

ركز هذا البحث على تقدير وقت البقاء لبيانات حقيقية لمرضى سرطان الثدي في محافظة نينوى للفترة من 2007 إلى 2013. تم اقتراح صيغ تقدير حصينة مع نموذج انحدار كوكس في تحليل البقاء وتحديد درجة الخطورة التي تواجهها المرأة المصابة بهذا المرض. حيث تم اقتراح استخدام بعض الأوزان الحصينة، وتم استبدال بعض مقدرات التباين التقليدية بمقدرات حصينة للوصول إلى تقدير فعال للنموذج، وكذلك اقتراح دوال وزن حصينة. كانت دالة الوزن هوبر هي الأفضل وتم تطبيقها مع القوالب الثلاثة للوصول إلى أفضل أنموذج شخص المتغيرات التي تؤثر على حدوث الحدث.

Miftahuddin Miftahuddin, Ziqratul Husna, Eddy Gunawan et al.

Farmer's Exchange Rate (FER) is one indicator to see the level of farmers' welfare. From 2014 to 2020, Aceh Province's FER was below 100 which indicates that farmers have not yet reached the level of welfare. This happens because of various factors including the price received by farmers (IR) is smaller than the price paid by farmers (IP). To find out the factors that influence the FER, it is necessary to do an analysis by forming a model. In this study, modeling of the FER data will be carried out, and see the factors that influence the index number with the longitudinal data regression approach. There are three estimation models, i.e. Common Effect Model, Fixed Effect Model, and Random Effect Model. Model selection of the best model is by using the Chow, Hausman, and Lagrange Multiplier tests. Furthermore, test the significance of the parameters using the simultaneous and partial tests and also see the value of the coefficient of determination (R2). The results obtained indicate that the appropriate model for the IR and IP data is the Random Effect Model where the R2for the IR and IP models are 67.06% and 85.42 respectively.

D. Dauitbek, Y. Nessipbayev, K. Tulenov

This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space LΦ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.

Wei Chun Ng , Michael B. C. Khoo, Zhi Lin Chong et al.

From the economic perspective, cost minimization is an important part of Statistical Process Control (SPC). The conventional approach in SPC focuses on monitoring the process mean and variance for possible shifts. In some processes, such as clinical and financial investments, the process mean and variance are not independent of one another. Thus, a separate monitoring of the mean and variance using two different control charts is not meaningful. Therefore, the coefficient of variation chart that measures the ratio of the process variance to the mean needs to be employed. In multivariate SPC, the quality characteristics that jointly control the process quality are correlated. Thus, the multivariate coefficient of variation (MCV) chart is used in process monitoring to monitor the process MCV. This work studies the economic and economic-statistical designs of the MCV chart. Optimal parameters that minimize the cost function of the MCV chart are computed. Furthermore, it is shown that adding statistical constraints to the economic design of the MCV chart improves the chart’s statistical performance with only a minimal increase in cost.

Bushra Khatoon, M. J. S. Khan, Zubdahe Noor

In this paper, the exact and explicit expressions for single, product, and conditional moments for inverted Kumaraswamy distribution using dual generalized order statistics (dgos) are derived. Further, the expression for maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for the parameters of inverted Kumaraswamy distribution based on dgos are deduced. Also, we obtained the results for order statistics and lower record values by putting some specific values of the parameters of dgos. Finally, a simulation study is carried out for illustrative purpose.

Robert E. Reys

Kazumi Wada, Mariko Kawano, Hiroe Tsubaki

In this paper, the performance of outlier detection methods has been evaluated with symmetrically distributed datasets. We choose four estimators, viz. modified Stahel-Donoho (MSD) estimators, blocked adaptive computationally efficient outlier nominators, minimum covariance determinant estimator obtained by a fast algorithm, and nearest-neighbour variance estimator, which are known for their good performance with elliptically distributed data, for practical applications in national survey data processing. We adopt the data model of multivariate skew-t distribution, of which only the direction of the main axis is skewed and contaminated with outliers following another probability distribution for evaluation. We conducted Monte Carlo simulation under the data distribution to compare the performance of outlier detection. We also explore the applicability of the selected methods for several accounting items in small and medium enterprise survey data. Accordingly, it was found that the MSD estimators are the most suitable.

Nur Fatihah Fauzi, Nurul Shahiera Ahmadi, Nor Hayati Shafii

The tourism industry in Malaysia has been growing significantly over the years. Tourism has been one of the major donors to Malaysia’s economy. Based on the report from the Department of Statistics, a total of domestic visitors in Malaysia were recorded at about 221.3 million in 2018 with an increase of 7.7% alongside a higher record in visitor arrivals and tourism expenditure.  This study aims to make a comparison between two methods, which are Fuzzy Time Series and Holt-Winter in forecasting the number of tourist arrival in Langkawi based on the monthly tourist arrival data from January 2015 to December 2019. Both models were generated using Microsoft Excel in obtaining the forecast value.  The Mean Square Error (MSE) has been calculated in this study to get the best model by looking at the lowest value. The result found that Holt-Winter has the lowest value that is 713524285 compared to the Fuzzy Time Series with a value of 2625517469. Thus, the Holt-Winter model is the best method and has been used to forecast the tourist arrival for the next 2 years. The forecast value for the years 2020 and 2021 are displayed by month.

M. A. Haq, G. Hamedani, M. Elgarhy et al.

We study a new distribution called the Marshall-Olkin Power Lomax distribution. A comprehensive account of its mathematical properties including explicit expressions for the ordinary moments, moment generating function, order statistics, Renyi entropy, and probability weighted moments are derived. The model parameters are estimated by the method of maximum likelihood. Monte Carlo simulation study is carried out to estimate the parameters and the performance of the estimates is judged via the average biases and mean squared error values. The usefulness of the proposed model is illustrated via real-life data set.

Hesham Reyad, M. Alizadeh, Farrukh Jamal et al.

Abstract We introduce a new class of continuous distributions called the Topp Leone odd Lindley-G family. Some mathematical properties of the new family such as; the raw and incomplete moments, moment generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of three applications to real data sets.

Ambrose Lo

ABSTRACT Calculating the expected values of different types of random variables is a central topic in mathematical statistics. Targeted toward students and instructors in both introductory probability and statistics courses and graduate-level measure-theoretic probability courses, this pedagogical note casts light on a general expectation formula stated in terms of distribution and survival functions of random variables and discusses its educational merits. Often consigned to an end-of-chapter exercise in mathematical statistics textbooks with minimal discussion and presented under superfluous technical assumptions, this unconventional expectation formula provides an invaluable opportunity for students to appreciate the geometric meaning of expectations, which is overlooked in most undergraduate and graduate curricula, and serves as an efficient tool for the calculation of expected values that could be much more laborious by traditional means. For students’ benefit, this formula deserves a thorough in-class treatment in conjunction with the teaching of expectations. Besides clarifying some commonly held misconceptions and showing the pedagogical value of the expectation formula, this note offers guidance for instructors on teaching the formula taking the background of the target student group into account.

Abbas Rahimi Foroushani, Seyyedeh Samira Mousavi, Kazem Mohammad

Background & Aim: Considering the psychosocial model of diseases, the aim of this study was to evaluate the effect of psychiatric intervention with regard to demographic and marriage characteristics on the pregnancy rate using Bayesian network model in infertile women. Methods & Materials: In a randomized clinical trial, 638 infertile patients referred to an infertility clinic were evaluated. Among them, 140 couples with different levels of depression in at least one of the spouses were included in this substudy. These couples were divided randomly into two groups. After psychiatric intervention the clinical pregnancy rates of the two groups. The data were divided into two groups: demographic characteristics and marriage specifications, and by drawing Bayesian networks using Grow-Shrink (GS) algorithm, the conditional probability of pregnancy was estimated. Results: According to the results, Bayesian network model of the GS algorithm was significant  (P = 0.548) and given that the fertility in the intervention group who were concurrently treated with antiretroviral treatment, the conditional probability was 38.5%, and this amount in the control group is 3.5% and group who were concurrently treated with induction of ovulation or did not receive any treatment the conditional probability was 72.2% and this amount in the control group is 23.1% comparing the values shows the importance of psychiatric intervention in increasing pregnancy rate. Conclusion: Results obtained from Bayesian network model are in line with results obtained from logistic model in terms of the significance of the variables with the difference that apart from the graphic structure, Bayesian network model also estimates conditional probabilities. This study shows that psychiatric and psychological treatments play an important role in curing infertility that will increase the chances of pregnancy.