This research paper presents a comprehensive investigation of novel Hardy-type dynamic inequalities that incorporate two independent weight functions, denoted as u and v. A distinctive feature of this work is its focus on time scales calculus with negative parameters, a generalization that unifies and extends discrete and continuous analysis. The basic methodology involves the application of the reverse Ho¨lder’s inequality and the Minkowski integral inequality to rigorously deduce all essential results. To illustrate the adaptability of our results, we provide explicit examples of the corresponding discrete and integral analogues for various time scales: when T=N (the natural numbers, indicating discrete sequences), T= lN0 for l > 1 (a quantum time scale), and T=R (the real numbers, signifying the classical continuous case). This paper situates its findings within a wider mathematical framework by demonstrating how they contain and extend certain cases of reverse Hardy-type dynamic inequalities previously formulated by distinguished scholars including Prokhorov, Kufner, Yang, Nguyen, and Benaissa. Consequently, this work presents a cohesive framework that broadens the theoretical terrain of Hardy-type inequalities.
In this paper, we propose new families of generalized inverse Pareto distributions using the T-R{Y} framework. Several choices of the distributions for the random variables T and Y give rise to generalized families of the random variable R, which in this paper is the inverse Pareto distribution. The generalized family of distributions is thus named as T-inverse Pareto{Y} family. We consider the exponential, Weibull, log-logistic, logistic, Cauchy, and extreme value distribution as potential choices for the distribution of the random variable Y. Specific members of the T-inverse Pareto{Y} family exhibit symmetric, skewed to the right, skewed to the left, unimodal, or bimodal density functions. Some statistical properties of the T-inverse Pareto{Y} family are investigated. The method of maximum likelihood is proposed for estimating the distribution parameters, and its performance is assessed using a simulation study. Three real data sets from different disciplines are analyzed to demonstrate the flexibility of the proposed T-inverse Pareto{Y} family of distributions.
The high accuracy of forecasts with the temperature data is very important to control environmental damages such as desertification and water resources drought as well as it is important to control the uses of renewable energy and clean energy. Using the multiplicative seasonal integrated auto-regressive and moving average (SARIMA) model for forecasting with uncertainty problem in the modeling process especially with nonlinear data such as minimum temperatures will make the forecasting results become low in quality because ARIMA is a linear model. Improving the minimum temperature forecasting quality is the main aim for this study by using more suitable methods for modeling the data with the problem of uncertainty. In this study, the minimum temperature data for Mosul and Baghdad will be used as a case of study. The state space (SS) will be used based on the ARIMA model which can be called the hybrid ARIMA-SS model which will be used to solve the uncertainty problem caused by the non-linearity of temperature data. Therefore the forecasting results may be not accurate. Also, the climate data often suffers from heterogeneity, especially in non-tropical regions, due to the high difference between the hot and cold seasons of these data. Time stratified (TS) will be used to solve the problem of data heterogeneity. In the ARIMA-SS hybrid method ARIMA is used only for the purpose of specifying the input of the SS model. In this study, the SS model was used as a statistical method for estimating and forecasting the state space. The SS method is to combine observations with current forecasts values by using weights that reduce biases and errors. The ARIMA-SS hybrid model has been used to deal with uncertainty and improve the minimum temperature forecasting by handling it well. The performance of the ARIMA model and the ARIMA-SS hybrid model will be compared to determine which of them will perform with more accurate forecasts .The results showed that the ARIMA-SS hybrid model outperformed the ARIMA model and produced more accurate forecasts. Therefore, it is possible to conclude that ARIMA-SS hybrid model can be used to result better forecasting accuracy for the minimum temperature compared to the forecasting performance of the traditional ARIMA model.
Saman Abdurrahman, Mochammad Idris, Faisal Faisal
et al.
In this paper, we present an application of fuzzy subset and fuzzy subgroup to a soft set and a soft group, thereby creating a soft set and a soft group within the same group. Furthermore, we refer to the soft and soft groups as level soft sets and level soft groups. We also found out the level of soft sets and the operations on soft sets, such as intersection, union, and subset. We also examine what conditions a fuzzy subgroup and a soft group must meet to form a level soft group. Moreover, we scrutinize the properties of operations on a soft set, specifically intersection, union, and AND, and apply them to the level soft group to ascertain if they consistently produce a level soft group over the same set. Furthermore, we investigate the formation of a level soft and level soft group resulting from the homomorphism of the group and soft group. The research findings can enrich studies on the relationships between structures in fuzzy subgroups and soft groups and the application of soft group levels in further research.
The importance of accurately forecasting extreme financial losses and their effects on the institutions involved in a given financial market has been highlighted by recent financial catastrophes. The flexibility with which econometric models can take into account the highly non-linear and asymmetric dependence in financial returns is a critical component of their capacity to forecast extreme events. Therefore, this study aims to forecast time-varying Value-at-Risk and expected shortfall dependence as a predictive density-based regime changes over time. To achieve this, a non-stationary Markov-switching generalized Autoregressive score model nested with copula is estimated using expectation–maximization (EM) algorithm. Extending this non-stationary model is quite challenging, as it requires specifications not only on how the usual parameters change over time but also those with mass distribution components. Dynamics of the estimated autoregressive score allowed the copula parameters to respond rapidly to time-varying key systemic parameters and risk. This is because regime changes are allowed to oscillated between high and low regimes. This is a clear indication of a regime shift in the parameters of an estimated model. Using the minimum score combining, six extreme value distributions are combined to the estimated MS(2)-GAS(1)-copula model and assessed the performance of each combined model 5 days and 30 days forecasting of value-at-risk and expected shortfall. The results of the forecasting performance indicated that the MS(2)-GAS(1)-GPD is the best model to model and forecast Value-at-risk and expected shortfall for the Botswana stock market. This is a promising technique for stochastic modeling of time-varying Value-at-Risk and Expected Shortfall. In addition, a foundation is provided for future researchers to conduct studies on emerging markets. These results are also important for risk managers and investors.
An admissible curve of a pseudo-Galilean space is said to be of constant-ratio if the ratio of the length of the tangent and normal components of its position vector function is a constant. In this paper, we investigate and characterize a spacelike admissible curve of constant-ratio in terms of its curvature functions in the pseudo-Galilean space G13. Also, we study some special curves of constantratio such as T-constant and N-constant types of these curves. Finally, we give some computational examples for constructing the meant curves to demonstrate our theoretical results.
If there is multicollinearity and outliers in the data, the inference about parameter estimation in the LS method will deviate due to the inefficiency of this method in estimating. To overcome these two problems simultaneously, it can be done using robust regression, one of which is ridge least absolute deviation method. This study aims to evaluate the performance of the ridge least absolute deviation method in surmounting multicollinearity in divers sample sizes and percentage of outliers using simulation data. The Monte Carlo study was designed in a multiple regression model with multicollinearity (ρ=0.99) between variables and and outliers 10%, 20%, 30% on response variables with different sample sizes (n = 25, 50,75,100,200; =0, and β=1 otherwise). The existence of multicollinearity in the data is done by calculating the correlation value between the independent variables and the VIF value. Outlier detection is done by using boxplot. Parameter estimation was carried out using the RLAD and LS methods. Furthermore, a comparison of the MSE values of the two methods is carried out to see which method is better in overcoming multicollinearity and outliers. The results showed that RLAD had a lower MSE than LS. This signifies that RLAD is more precise in estimating the regression coefficients for each sample size and various outlier levels studied.
This article demonstrates how data from a biology paper, which analyzes the relationship between mass and metabolic rate for two species of marine bryozoan, can be used to teach a variety of regression topics to both introductory and advanced students. A thorough analysis requires intelligent data wrangling, variable transformations, and accounting for correlation between observations. The bryozoan data can be used as a valuable class example throughout the semester, or as a dataset for extended homework assignments and class projects. Supplementary materials for this article are available online.
Probabilities. Mathematical statistics, Special aspects of education
The safety of underground structure under seismic load is an important basis of the normal operation of underground rail transit system. Structural seismic vulnerability assessment based on incremental dynamic analysis method can evaluate the probability of the structure exceeding a certain limit state under a specific seismic intensity in terms of probability. In this paper, the seismic vulnerability of a multi-storey subway station structure is evaluated using this method, and a two-dimensional finite element model of both soil and structure is established by finite element software ABAQUS. The vulnerability curve is obtained through incremental dynamic analysis and mathematical statistics. Based on this curve, the probabilities of the structure exceeding four seismic limit states are obtained under the design seismic intensity and the rarely occurred seismic intensity at 7 degree. Results show that this station may attain slight damage under design seismic intensity of 7 degree, and may attain life safety at the rarely occurred seismic intensity at 7 degree.
Martin M. Kithinji, Peter N. Mwita, Ananda O. Kube
In this paper, we propose an extreme conditional quantile estimator. Derivation of the estimator is based on extreme quantile autoregression. A noncrossing restriction is added during estimation to avert possible quantile crossing. Consistency of the estimator is derived, and simulation results to support its validity are also presented. Using Average Root Mean Squared Error (ARMSE), we compare the performance of our estimator with the performances of two existing extreme conditional quantile estimators. Backtest results of the one-day-ahead conditional Value at Risk forecasts are also given.
When a financial derivative can be traded consecutively and its terminal payoffs can be adjusted into a stationary time series, there might be a statistical arbitrage opportunity even under the efficient market hypothesis. In particular, we show the examples of selling put options of the three major ETFs (Exchange Traded Funds) in the U.S. market.
To begin, we find certain formulas Q(k,α)=G1k(α)G2k(α), for k=-1,0,1,…,9. These yield that part of the total separability probability, P(k,α), for generalized (real, complex, quaternionic, etc.) two-qubit states endowed with random induced measure, for which the determinantal inequality ρPT>ρ holds. Here ρ denotes a 4×4 density matrix, obtained by tracing over the pure states in 4×(4+k)-dimensions, and ρPT denotes its partial transpose. Further, α is a Dyson-index-like parameter with α=1 for the standard (15-dimensional) convex set of (complex) two-qubit states. For k=0, we obtain the previously reported Hilbert-Schmidt formulas, with Q(0,1/2)=29/128 (the real case), Q(0,1)=4/33 (the standard complex case), and Q(0,2)=13/323 (the quaternionic case), the three simply equalling P(0,α)/2. The factors G2k(α) are sums of polynomial-weighted generalized hypergeometric functions pFp-1, p≥7, all with argument z=27/64=(3/4)3. We find number-theoretic-based formulas for the upper (uik) and lower (bik) parameter sets of these functions and, then, equivalently express G2k(α) in terms of first-order difference equations. Applications of Zeilberger’s algorithm yield “concise” forms of Q(-1,α), Q(1,α), and Q(3,α), parallel to the one obtained previously (Slater 2013) for P(0,α)=2Q(0,α). For nonnegative half-integer and integer values of α, Q(k,α) (as well as P(k,α)) has descending roots starting at k=-α-1. Then, we (Dunkl and I) construct a remarkably compact (hypergeometric) form for Q(k,α) itself. The possibility of an analogous “master” formula for P(k,α) is, then, investigated, and a number of interesting results are found.
Ertefaie Ashkan, Asgharian Masoud, Stephens David A.
In the causal adjustment setting, variable selection techniques based only on the outcome or only on the treatment allocation model can result in the omission of confounders and hence may lead to bias, or the inclusion of spurious variables and hence cause variance inflation, in estimation of the treatment effect. We propose a variable selection method using a penalized objective function that is based on both the outcome and treatment assignment models. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some mild conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. Using the proposed method we analyze a set of data on economic growth and study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita.
Malaysia is currently facing low production of palm fruit. The poor palm fruit output will inevitably affect
the economy in Malaysia. Hence, the government related agency needs to find effective ways to increase
the production of palm fruit. Factors that affect the production of palm fruit include palm tree planted
area and quantity of the crop. This paper proposes the Goal Programming approach to maximize the
production of palm fruit. The approach maximized the planted area for three rural areas and increases
the number of palm fruit crop for three rural areas. This approach is used to find optimal solution to the
low palm fruit output. The findings show that all the study objectives have been fully achieved. The
proposed planted area available from the QM Windows 4.0 software can increase up to 75% from the
existing planted area availability for three rural areas in Jengka, Pahang.
For the analysis of square contingency tables with the same row and column ordinal classications, this article proposes a new model which indicates that the log-ratios of symmetric cell probabilities are proportional to the difference between log-row category and log-column category. The proposed model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate log-normal distribution. Also, this article gives the decomposition of the symmetry model using the proposed model with the orthogonality of test statistics. Examples are given. The simulation studies based on bivariate log-normal distribution are given.
This paper surveys various statistical methods that have been proposed for the examination of the efficiency of financial markets and proposes a novel procedure for testing the predictability of a time series. For illustration, this procedure is applied to Austrian stock return series.
This paper deals with modelling income distributions in the Czech Republic in 1992–2007. The net annual income per capita for Czech households is evaluated from data based on the microcensus and the EU-SILC 2005–2008. For all analysed years the distribution of incomes was estimated in the whole sample as well as in the subgroup of households, whose heads are physicists (or experts in related sciences), architects and engineers. In
the paper the three-parametric lognormal distribution is used as a model. Unknown
parameters are estimated with the use of four methods – those of maximum likelihood, quantiles, moments and L-moments.