Power Transformation Method Research Articles

The power new XLindley distribution: Statistical inference, fuzzy reliability, and applications

This paper introduces the power new XLindley (PNXL) distribution, a novel two-parameter distribution derived using the power transformation method applied to the XLindley distribution. We thoroughly explore the structural properties of the PNXL distribution, including the rth moment about the origin, moment generating function, survival rate function, distribution function, hazard rate function, skewness, kurtosis, and coefficient of variation. Additionally, we derive the quantile function, fuzzy reliability, reliability measures, stochastic ordering, and actuarial measures for this new distribution. To estimate the parameters of the PNXL distribution, we propose several estimators and evaluate their performance through extensive simulation studies. To demonstrate the applicability and superiority of the PNXL distribution over existing distributions, we fit it to two real datasets and compare its performance with potential competing models. The results highlight the PNXL distribution's effectiveness and potential as a robust tool for modeling and analyzing real-world data.

Alpha power inverse Weibull distribution: A new lifetime distribution with application to gastric cancer data

Lifetime data analysis has an essential role in various fields of science. In general, lifetime data have a skewed distribution pattern. The Weibull distribution is one of the most frequently used distributions for modeling lifetime data. However, the Weibull distribution is not suitable for modeling data with non-monotonous hazard functions, one of which is an upside-down bathtub shape. According to Sharma et al. (2015), the inverse version of several probability distributions can model the data with an upside-down bathtub shape, one of which is the inverse Weibull distribution. This paper explains the Alpha Power Inverse Weibull (APIW) distribution as a generalization version of the inverse Weibull distribution. This distribution is constructed by using the Alpha Power Transformation method. The modification is done by adding a shape parameter to the inverse Weibull distribution to increase flexibility. The characteristics of APIW distribution discussed include probability density function, distribution function, survival function, hazard function, and the r-th moment. The probability density function of APIW distribution is left-skewed and unimodal. In addition, the hazard function of APIW distribution has an upside-down bathtub shape. The parameters of this distribution are estimated by the maximum likelihood method. Finally, for illustration purposes, the data about the time until gastric cancer patients die are modelled with the inverse Weibull distribution, and the APIW distribution is given. The modeling result shows that the Alpha Power Inverse Weibull distribution is better at modeling the time until gastric cancer patients die data than the inverse Weibull distribution.

Power unit Gumbel type II distribution: Statistical properties, regression analysis, and applications

Using the power transformation method, we introduce a generalized version of the unit Gumbel type-2 distribution. The new lifetime distribution is called the power unit Gumbel type-2 distribution (PUGT2D). The new distribution’s statistical and reliability properties are given, and some estimation methods are proposed for estimating the model parameters. The usefulness and flexibility of the new distribution are illustrated with real datasets. Results based on log-likelihood, information statistics, and goodness-of-fit test results showed that the PUGT2D better fits the data than the other competing distributions. Moreover, a new regression model based on the new distribution is introduced and demonstrated to exhibit superior applicability through a numerical example.

A New Class of Generalized Extreme Value Distribution and Application under Alpha Power Transformation Method

This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness.

Climate change in the upper Awash subbasin and its possible impacts on the stream flow, Oromiyaa, Ethiopia

ABSTRACT Modelling climate change impact is very important to reduce the crisis behind food security, drought, and loss of energy sectors. The impact on streamflow and hydrological components due to climate change was aimed to investigate by the SWAT model for this study. Two regional climate models (RCM) were selected according to their performance to calibrate and validate the streamflow. The Regional Climate Models’ performance in simulation of flow and the hydrological cycle was evaluated by statistical performance criteria. Digital elevation model (DEM), land use land cover and soil map, and streamflow data were collected and used as raw input for the model. Bias correction was made by using power transformation and variance scaling method for RCM against observed data. The result simulated with RACMO22T was best with (PBIAS = 0.23, NSE = 0.84, R2 = 0.79) for calibration, (PBIAS = 0.11, NSE = 0.88, R2 = 0.81) for validation. RCA4 model underperformed in simulating streamflow compared to RACMO22T with (PBIAS = 0.28, NSE = 0.78, R2 = 0.74) and (PBIAS = 0.18, NSE = 0.85, R2 = 0.78) for calibration and validation of the models respectively. The streamflow was projected and shows a slightly increasing trend respectively with 13.8 and 21.3 % for the 2030s and 2050s simulation years. But in the 2080s simulation periods, the simulated streamflow indicates a decreasing trend under representative concentration pathways (RCP4.5) by 12.5%. The overall result indicates both streamflow and runoff show a decreasing pattern in the end of this century under both scenarios. The spatial variability of hydrological components which contributes to streamflow was dependent on the subbasin characteristics. Furthermore, the simulated groundwater recharge (GW_Q), rainfall, water yields (WYLD), surface runoff (SUR_Q) and evapotranspiration (ET) were decreased by 4%, 17.7%, 20.8%, 27.7%, and 8.6% respectively for the baseline period.

A New Approach to Production Process Capability Assessment for Non-Normal Data

The process quality capability indicators Cp and Cpk are widely used to measure process capability. Traditional metric estimation methods require process data to be explicit and normally distributed. Often, the actual data obtained from the production process regarding the measurements of quality features are incomplete and do not have a normal distribution. This means that the use of traditional methods of estimating Cp and Cpk indicators may lead to erroneous results. Moreover, in the case of qualitative characteristics where a two-sided tolerance limit is specified, it should not be very difficult. The problem arises when the data do not meet the postulate of normality distribution and/or a one-sided tolerance limit has been defined for the process. Therefore, the purpose of this article was to present the possibility of using the Six Sigma method in relation to numerical data that do not meet the postulate of normality of distribution. The paper proposes a power transformation method using multiple-criteria decision analysis (MCDA) for the asymmetry coefficient and kurtosis coefficient. The task was to minimize the Jarque–Bera statistic, which we used to test the normality of the distribution. An appropriate methodology was developed for this purpose and presented on an empirical example. In addition, for the variable after transformation, for which the one-sided tolerance limit was determined, selected process quality evaluation indices were calculated.

The Power Zeghdoudi Distribution: Properties, Estimation, and Applications to Real Right-Censored Data

A new two-parameter power Zeghdoudi distribution (PZD) is suggested as a modification of the Zeghdoudi distribution using the power transformation method. As a result, the PZD may have increasing, decreasing, and unimodal probability density function and decreasing mean residual life function. In addition, other properties are presented, such as moments, order statistics, reliability measures, Bonferroni and Lorenz curves, Gini index, stochastic ordering, mean and median deviations, and quantile function. Following this, a section is devoted to the related model parameters which are estimated using the maximum likelihood estimation method, the weighted least squares and least squares methods, the maximum product of spacing method, the Cramer–von Mises method, and the right-tail and left-tail Anderson–Darling methods, and the Nikulin–Rao–Robson test statistic is considered. A simulation study is conducted to assess these methods and to investigate the distribution properties with right-censored data. The applicability of the proposed model is studied based on three real data sets of failure times, bladder cancer patients, and glass fiber data with a comparison with such competitors as the gamma, xgamma, Lomax, Darna, power Darna, power Lindley, and exponentiated power Lindley models. According to several established criteria, the comparative findings are overwhelmingly favorable to the suggested model.

Application of artificial intelligence image recognition technology based on Faster-R CNN in automatic inspection of power transmission and transformation

In order to effectively improve the work efficiency and real-time performance of an automatic inspection of power transmission and transformation, this paper studies the automatic inspection method of power transmission and transformation based on artificial intelligence image recognition technology. First, we use cameras and unmanned aerial vehicles (UAVs) to obtain image data for power transmission and transformation inspection. Second, through the artificial sample calibration and reconstruction technology, the power transmission, and transformation inspection sample database is constructed. Then, the model is trained using the Faster-R CNN algorithm based on regional relationship features. Finally, the model is further optimized through model release and evaluation to realize intelligent diagnosis in power transmission and transformation detection. This research raises the recognition accuracy of power transmission and transformation inspection, improves the intelligence and efficiency of inspection, and provides good technical support for the construction of intelligent operation inspection.

Bias-Corrected IDF Curves From Satellite-Based Rainfall for HoaBinh Province, Vietnam

Satellite-based rainfall is extremely valuable data to quantify the probability of occurrence of rainfall events but is still uncertain to a certain extent. Therefore, this study firstly evaluates the performance of the satellite-based rainfall, PERSIANN-CCS, with rain gauge rainfall. The power transformation method is then applied to correct the satellite-based rainfall. Importantly, the Intensity-Duration-Frequency (IDF) curves are then constructed with the return periods of 5, 10, 25, 50, 100 and 200 years using the Gumbel probability distribution. The results show an efficiency of power transformation on satellite-based rainfall for both rainfall amount and events. It is especially noticed that it is well matched between bias-corrected satellite-based and rain gauge IDF curves duration 12-, 24-, 48- and 72-hour as a particular. For the duration of less than 12-hour, satellite-based IDF curves without bias correction significantly fit the rain-gauge IDF curves within the considered periods.

A Generalized Form of Power Transformation on Exponential Family of Distribution with Properties and Application

In this paper, we proposed a new generalized family of distribution namely new alpha power Exponential (NAPE) distribution based on the new alpha power transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties of the proposed distribution are obtained including moment, incomplete moment, conditional moment, probability weighted moments (PWMs), quantile function, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics. The percentage point of NAPE distribution for some specific values of the parameters is also obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters of NAPE distribution. A simulation study has been performed to evaluate and execute the behavior of the estimated parameters for mean square errors (MSEs) and bias. Finally, the efficiency and flexibility of the new proposed model are illustrated by analyzing three real-life data sets.

Discussion on Selection Method of Power Transformation and Distribution and Generator System for Different Grade Data Centers

Discussion on Selection Method of Power Transformation and Distribution and Generator System for Different Grade Data Centers

A novel extension of Gumbel distribution: Statistical inference with Covid-19 application

This paper introduced a relatively new statistical model as an extension of Gumbel distribution, which combines the new alpha power transformation method and Gumbel distribution. Different statistical properties of the proposed model were derived mathematically. Different estimation methods were introduced to estimate proposed model parameters. The behavior of these parameters was checked by using randomly generated data sets and the introduced estimation methods. Two real data sets were analyzed to show how the proposed model fits this data sets than its baseline model and many other well-known and related models.

A new weighted version of alpha power transformation method: properties and applications to COVID-19 and software reliability data

This paper is an effort to propose a new method to generate probability distributions based on alpha power transformation method for more flexibility. We refer to the new method as modified alpha power transformed method. The new proposed method can be considered as a weighted version of the alpha power transformation method with more ability to model various types of data. A special case has been studied in detail namely; one parameter exponential distribution. The new generalization of the traditional exponential distribution provides a better fit than the exponential distribution and some competitive models. It appears to be a distribution capable of allowing constant, decreasing and increasing hazard rates based on its parameters. Various properties of the new method as well as the new distribution are derived, including explicit expressions for the quantiles, moments, moment generating function and expression of entropies. The point and interval estimations are investigated using maximum likelihood method. A simulation study is carried out and two applications, one for COVID-19 data and the other for software reliability data are considered to show the flexibility of the proposed distribution. The results show that the new distribution provides a better fit than some other competitive distributions including exponential, alpha power exponential, Weibull and gamma distributions.

A new generalization of the inverse Lomax distribution with statistical properties and applications

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.

Alpha Power Lomax Distribution: Properties and Application

This study offers a newly proposed distribution called alpha power Lomax (APL) distribution as a new extension of the Lomax distribution using the alpha power transformation (APT) method. Some distributional properties of newly defined distribution such as density function, moments, hazard and survival functions, orders statistics etc. are investigated. Parameters of the APL distribution are estimated with the help of the maximum likelihood (ML) estimation method. The applicability of the APL distribution is conducted through a simulation study and a real data example.

A data-driven intelligent hybrid method for health prognosis of lithium-ion batteries

For estimation of the RUL (Remaining useful life) of Lithium ion battery we are required to do its health assessment using online facilities. For identifying the health of a battery its internal resistance and storage capacity plays the major role. However the estimation of both these parameters is not an easy job and requires lot of computational work to be done. So to overcome this constraint an easy alternate way is simulated in the paper through which we can estimate the RUL. For formation of a linear relationship between health index of the battery (HI) and its actual capacity used of power transformation method is done and later on to validate the result a comparison study is done with Pearson & Spearman methods. Transformed value of Health Index is used for developing a neural network. The results demonstrated in the paper shows the feasibility of the proposed technique resulting in great saving of time

Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

Optimal imputation of the missing data using multi auxiliary information

This article deals with some new imputation methods by extending the work of Bhushan and Pandey using multi-auxiliary information. The popularly used imputation like mean imputation, ratio method of imputation, regression method of imputation and power transformation method are special cases of the proposed methods apart from being less efficient than the proposed methods. The proposed imputation methods can be considered as an efficient extension to the work of Singh and Deo (Stat Pap 44:555–579, 2003), Singh (Stat A J Theor Appl Stat 43(5):499–511, 2009), Ahmed et al. (Stat Transit 7(6):1247–1264, 2006), Diana and Perri (Commun Stat Theory Methods 39:3245–3251, 2010) and Bhushan and Pandey (J Stat Manag Syst 19(6):755–769, 2016, Commun Stat Theory Methods 47(11):2576–2589, 2018). The theoretical results are derived and comparative study is conducted using real and simulated data and the results are found to be quite encouraging providing the improvement over the all discuss work.

GCM selection and temperature projection of Nigeria under different RCPs of the CMIP5 GCMS

The possible future changes in temperature over Nigeria were projected in this study. Using Climate Research Unit (CRU) temperature as the reference data, gain ratio (GR), entropy gain (EG), and symmetrical uncertainty (SU) feature selection methods and a multi-criteria decision-making (MCDM) approach were used in selecting the most suitable GCMs for Nigeria from 20 Coupled Model Intercomparison Project phase 5 (CMIP5) global climate models (GCMs). The biases in selected GCMs were corrected using power transformation (PT) method. Multi-model ensembles (MMEs) were generated for the selected GCMs for the different temperature classes’ maximum, average, and minimum for all RCPs. The MMEs were used for the projection of temperatures over the country during 2010–2039, 2040–2069, and 2070–2099. The GCMs HadGEM2-ES, CESM1-CAM5, CSIRO-Mk3.6.0, and MRI-CGCM3 were the best performing in replicating temperature characteristics of the observed temperature in Nigeria. The MME mean projections of bias-corrected (BC) GCMs using PT revealed that there will be an increase in temperature of 4.0 °C at the semi-arid and 5.0 °C at the arid regions during dry and wet seasons respectively under RCP 4.5. In the same regions, the maximum temperature is expected to increase up to 5.5 °C under RCP 8.5 during 2070–2099 in the dry season. In the wet season, temperatures are expected to be higher under RCP 8.5, with an increase of 0.0–4.0 °C in the southern region and 3.0–6.9 °C in the northern region.

Network Diffusion Promotes the Integrative Analysis of Multiple Omics.

The development of integrative methods is one of the main challenges in bioinformatics. Network-based methods for the analysis of multiple gene-centered datasets take into account known and/or inferred relations between genes. In the last decades, the mathematical machinery of network diffusion—also referred to as network propagation—has been exploited in several network-based pipelines, thanks to its ability of amplifying association between genes that lie in network proximity. Indeed, network diffusion provides a quantitative estimation of network proximity between genes associated with one or more different data types, from simple binary vectors to real vectors. Therefore, this powerful data transformation method has also been increasingly used in integrative analyses of multiple collections of biological scores and/or one or more interaction networks. We present an overview of the state of the art of bioinformatics pipelines that use network diffusion processes for the integrative analysis of omics data. We discuss the fundamental ways in which network diffusion is exploited, open issues and potential developments in the field. Current trends suggest that network diffusion is a tool of broad utility in omics data analysis. It is reasonable to think that it will continue to be used and further refined as new data types arise (e.g. single cell datasets) and the identification of system-level patterns will be considered more and more important in omics data analysis.