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The basic principle of the classical work of wavelet methods is that the empirical wavelet coefficients are shrunk, thresholded, or both shrunk and threshold level by level based on their volumes. A block wavelet shrinkage strategy that depends on neighboring coefficients, where the wavelet coefficients are divided into multiple groups, is proposed. That means the thresholding of coefficients in the middle of each block depends on the whole block’s data using the decimated wavelet method. The NeighBlock procedure combines the previously found advantages for block thresholding methods with those obtained using information about neighboring coefficients. In this article, we collect an image corrupted with level of noise, then applying Block method to remove the noise. More precisely, the construction is started from collecting image, computing wavelet coefficients, applying the method, then inverse the wavelet coefficients. Wavelet shrinkage is a practical case in regression techniques, particularly when the unknown image has distinctive features; this might cause an unsuitable picture. The biggest challenge in the image is to calculate the wavelet coefficients and to invert these coefficients to the image after treatment. To solve this problem two functions based on the Haar wavelet are built to compute these coefficients and then invert the wavelet coefficients to provide the estimate image. The main idea of a wavelet is to translate a given image to a discrete wavelet transform (DWT) which is usually corrupted by noise; shrink or thresh the wavelet coefficients to decrease the noise impact, then invert the DWT to calculate the proper unknown image. The difference between these tools is that shrinking changes the wavelet coefficients of individual magnitudes, while the thresh keeps shrinking or threshold wavelet coefficients towards zero. The main goal is to compere the proposed method to state-of-the-art methods, and show that the proposed method provides good denoising performance. The asymptotic and numerical performances of the proposed method of the estimator are investigated. In numerical comparisons with different approaches, the proposed estimator method performs excellently. We propose decimated wavelet shrinkage techniques based on neighboring coefficients. Extensive simulations demonstrate that techniques almost always give insignificant results than the classical method for the image.

Researchers can use many statistical tools to fit data, either simple or complex, based on the likelihood. However, more parameters usually provide a smooth resolution, due to the order of likelihood increases, however, the main issue is to use special tools to estimate parameters. For example, we are used the process capability indices (CL) for measuring the performance of a process with, lower specification limit L). The article adopts a method of CL when the unit’s lifetime has two parameters generalised half-logistic lifetime population. The real-world dataset is collected with respected to Type-I generalised hybrid censoring scheme. The scale parameter is specified under data transformation technology. The Bayes and maximum likelihood estimators are formulated using the conjugate form of the prior and examined using the squared error loss procedure. The developed estimators construct credible and confidence intervals for CL. Real world examples in this article illustrate the pattern of the estimate value of confidence interval for the parameter CL and the interval estimations of CL are assessed by a Monte Carlo simulation studies.

This paper proposes a new family of estimators for population mean with a non-response using a simple random sampling. It specifically applies this method to estimate the mean in Turkey’s Education sector data sets, accounting for non-response. The study integrates additional information in the form of mean and cdf of the auxiliary variable which is highly positively correlated with the study variable to develop a general class of estimators tailored for the non-response using a simple random sampling scheme. Through numerical research, the characteristics of these estimators – namely, their biases and mean square errors – have been carefully investigated and deeply evaluated. The basic estimator of a population mean is under-performed by the suggested estimators. The empirical investigation validates the results, demonstrating the improved relative efficiency of the proposed estimator over the existing estimators, as demonstrated by theoretical and numerical comparisons.

Abstract The control charts are frequently employed in process monitoring to assess the average and variability of a process, assuming a normal distribution. However, it is worth noting that some process distributions tend to exhibit a positively skewed distribution, such as the lognormal distribution. This article proposed a maximum exponential weighted moving average control chart for joint monitoring of mean and variance under a lognormal process. The proposed control chart is evaluated by using the run length profile such as ARL and SDRL. The Monte Carlo simulation is conducted by using the R language to find the run length profile. An application is presented to demonstrate the design of the proposed control chart.

We consider and implement a new contemporary and state-of-the-art probabilistic model with optimal data modeling capabilities. We call the present probabilistic model a new beta power flexible Weibull distribution. It is obtained by using the flexible Weibull distribution together with the new beta power transformed method. The flexibility of the new model is explored visually. The visual inspection shows that the proposed model captures many important forms (or shapes) of its density and hazard rate function. For the new beta power flexible Weibull distribution, the point estimators are derived mathematically and numerically (using practical data sets). Additionally, simulation studies are also exercised to show that these point estimators are efficient and consistent. Ultimately, three data sets are taken into account to certify the optimality and relevance of the new model. Among the data sets, the first two applications are picked from reliability engineering and the third data set is observed from music engineering. Regarding the fitting of these three data sets, taking into consideration for statistical tests, it is distinguished that the new model persistently outstrips the rival distributions.

In today's modern world, marketing is a fruitful source to grow a business by reaching a larger audience. This paper considers a popular social media source called LinkedIn.com as a way of marketing or reaching a larger audience. We consider a regression approach to explore the statistically significant role of the LinkedIn medium as a tool for reaching a larger audience. In addition to statistically exploring the role of the LinkedIn medium in the financial sector, we also introduce a new Weibull-based probability distribution, namely, the exponential TX inverse Weibull (for short'ETXI-Weibull') distribution. The ETXI-Weibull distribution is specially designed for analyzing LinkedIn marketing data. The beauty of the ETXI-Weibull distribution is that it satisfies the heavy-tailed characteristics, which are explored visually and mathematically. For the ETXI-Weibull distribution, the estimators are derived whose performances are evaluated visually and numerically through a simulation study. The ETXI-Weibull distribution is applied practically by considering the LinkedIn marketing data set as an example. Using certain established statistical tests, we observe that the ETXI-Weibull distribution provides an optimal fit to the LinkedIn marketing data set. Furthermore, a bivariate extension of the exponential TX inverse Weibull model is also introduced. Finally, the bivariate extension of the exponential TX inverse Weibull model is illustrated by modeling the LinkedIn marketing and sales data.

This paper addresses some classes of combined and separate imputation methods (CSIMs) of the population mean under stratified simple random sampling (SSRS) along with their characteristics. To the best of our knowledge, these imputation methods (IMs) have yet not been studied by any author under SSRS, hence these IMs are called ‘novel’. In addition, the existing CSIMs are distinguished as the members of the suggested CSIMs, respectively. The theoretical conditions under which the proposed IMs perform better are obtained by comparing the proposed IMs with the existing IMs. To validate the theoretical findings, the numerical and simulation studies are conducted on real and artificial populations, respectively.

In this article, we offer simple random sampling (SRS) based efficient class of estimators of population mean Y¯ utilizing additional information. The expression of the mean square error of the proposed class of estimators is deduced up to first degree approximation. The efficiency conditions are established which are enhanced numerically utilizing a simulation study consummated over symmetrical and asymmetrical populations. Real data sets are also utilized to exemplify the suggested estimators. The numerical findings are appeared rather acceptable demonstrating better advancement over the ordinary estimators.

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets.

The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of expected shortfall regression with an expectile risk model. A spatio-functional Nadaraya–Watson estimator of the studied metric risk is constructed. The main asymptotic results of this work are the establishment of almost complete convergence under a mixed spatial structure. The claimed asymptotic result is obtained under standard assumptions covering the double functionality of the model as well as the data. The impact of the spatial interaction of the data in the proposed risk metric is evaluated using simulated data. A real experiment was conducted to measure the feasibility of the Spatio-Functional Expectile Shortfall Regression (SFESR) in practice.

This paper treats the problem of risk management through a new conditional expected shortfall function. The new risk metric is defined by the expectile as the shortfall threshold. A nonparametric estimator based on the Nadaraya–Watson approach is constructed. The asymptotic property of the constructed estimator is established using a functional time-series structure. We adopt some concentration inequalities to fit this complex structure and to precisely determine the convergence rate of the estimator. The easy implantation of the new risk metric is shown through real and simulated data. Specifically, we show the feasibility of the new model as a risk tool by examining its sensitivity to the fluctuation in financial time-series data. Finally, a comparative study between the new shortfall and the standard one is conducted using real data.

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. We construct an estimator of this new model using the k-nearest neighbors (kNN) smoothing approach. The mathematical properties of the constructed estimator are stated through the establishment of the pointwise complete convergence. Additionally, we prove that the constructed estimator is uniformly consistent over the nearest neighbors (UCNN). Such asymptotic results constitute a good mathematical support of the proposed financial risk process. Thus, we examine the easy implantation of this process through an artificial and real data. Our empirical analysis confirms the superiority of the kNN-approach over the kernel method as well as the superiority of the expectile over the quantile in financial risk analysis.

Russia and Ukraine got into an armed conflict on 24th February 2022. In addition, the World Health Organisation still warns of a fast growth in infections and deaths. Infectious disease remains a serious issue in Ukraine and poorly governed cities, such as those in armed conflicts. During this period of security instability, the coronavirus situation in Ukraine is alarming and needs more attention. In this context, our focus in the current work is to model COVID-19 spread risk from Ukrainian international refugees in neighboring countries. This study aims to estimate the number of daily coronavirus cases among Ukrainian international refugees for informed decisions for the pandemics' spread risk. For that reason, we used “Coronavirus Pandemic (COVID-19)” data from “Our World in Data” (from 2020-03-03 to 2022-02-22) and the data about Ukrainian International Refugees provided by United Nations High Commissioner for Refugees related (from 2022-02-22 to 2022-03-11). We performed ARIMA, TBATS, and ETS and selected the best model. Through a cross-validation process, the findings revealed that around 6 individuals [95% CI: 5%–7%] over 10,000 Ukrainian international refugees are likely COVID-19 cases. ARIMA is the best model to fit the Ukrainian daily number of cases among the refugees fleeing the crisis. On average, they are daily 100 possible COVID-19 cases among Ukrainian international refugees and authorities and humanitarian actors need be informed decisions to control the pandemic and support refugees effectively.

Abstract This article presents and investigates a modified version of the Weibull distribution that incorporates four parameters and can effectively represent a hazard rate function with a shape resembling a bathtub. Its significance in the fields of lifetime and reliability stems from its ability to model both increasing and decreasing failure rates. The proposed distribution encompasses several well-known models such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh, and modified Weibull distributions. The paper derives key mathematical statistics of the proposed distribution, including the quantile function, moments, moment-generating function, and order statistics density. Various mathematical properties of the proposed model are established, and the unknown parameters of the distribution are estimated using different estimation techniques. Furthermore, the effectiveness of these estimators is assessed through numerical simulation studies. Finally, the paper applies the new model and compares it with various existing distributions by analyzing two real-life time data sets.

The usefulness of a new heavy-tailed distribution is studied in this article. The type-I heavy-tailed exponential (TI-HTE) distribution studied here has been suggested in the literature but has not been studied anywhere other than now. Some of its properties, together with graphical representations, were considered. The study utilized the maximum likelihood method in the estimation of the parameters. The primary goal is to create group acceptance sampling plans (GASP) using the TI-HTE model to determine whether units from a production process should be accepted or rejected. Through simulation studies and real-world examples, the importance of the TI-HTE model in identifying extreme behaviors beyond typical distributions like exponential or heavy-tailed distributions is emphasized.

This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data.

It is a deep-rooted and already observed reality that probabilistic models play an important role in describing and explaining the events/situations under consideration. Focusing attention on the fundamental role and applicability of the probabilistic models, this article considers the development of a new probability model derived through the implementation of a trigonometric function. The suggested model is named as a new cosine flexible Weibull (NCF-Weibull) distribution. This model is accomplished by exploiting the cosine functional approach. Some statistical characteristics of the NCF-Weibull distribution are given. Alongside, the estimates of the NCF-Weibull model are also obtained. Besides them, a simulation study for different settings of the parameter values of the NCF-Weibull model is also provided. Through the simulation study it is evidenced that the estimators of the NCF-Weibull distribution consistently perform well in terms of stability, consistency, and efficiency. Finally, the optimality of the NCF-Weibull distribution is judged by using two applications from different sectors. Based on five evaluation criteria alongside the p-value, the NCF-Weibull distribution shows optimal performances for both data sets.

This work considers the Local Linear Estimation (LLE) of the conditional functional mean. This regression model is used when the independent variable is functional, and the dependent one is a censored scalar variable. Under standard postulates, we establish the asymptotic distribution of the LLE by proving its asymptotic normality. The obtained results show the superiority of the LLE approach over the functional local constant one. The feasibility of the studied model is demonstrated using artificial data. Finally, the usefulness of the obtained asymptotic distribution in incomplete functional data is highlighted through a real data application.