Cramer-von Mises Research Articles

Analyzing Cancer Survival Times Using the Exponentiated Fréchet-Gompertz Distribution

Understanding the survival of cancer patients is essential for determining optimal treatment strategies. This research introduces a robust distribution for analyzing survival data known as the Exponential Fr ́echet-Gompertz distribution (EFG). The EFG combines the unique characteristics of the Exponential Fr ́echet and Gompertz distributions, enhancing its efficiency and providing greater flexibility in representing complex datasets. The study specifically investigates the EFG distribution’s effectiveness in modeling cancer patients’ survival times. A comprehensive analysis of the distribution’s properties is presented, including the quantile and quartile functions, shape indices, moments, moment-generating function, characteristic function, mean residual life, mean waiting time, R ́enyi entropy, and order statistics. The parameters of the distribution are derivedusing five distinct methods: Maximum Likelihood Estimation (MLE), Ordinary Least Squares (OLS), Weighted Least Squares (WLS), Cram ́er-von Mises (CVM), and Maximum Product of Spacings (MPS). A Monte Carlo simulation technique is employed to evaluate the performance of these estimation methods. The simulation results indicate that as sample size increases, the meansquare error (MSE) values for all estimators decrease. Notably, the MLE exhibits the lowest MSE, while the MPS has the highest MSE, particularly for smaller sample sizes. Furthermore, the study presents a comprehensive comparison of the effectiveness of these estimation methods in analyzing survival times for various cancer types, including bladder, bone, blood and brain cancer. The results indicate that the EFG distribution is an optimal model for representing the survival times of patients across these different cancers data. Furthermore, the W.LS method yielded superior estimations for most datasets concerning cancer patient survival. Overall, the EFG distribution demonstrates exceptional capability in accurately fitting survival times for cancer patients compared to other competing distributions.

Statistical Analysis and Several Estimation Methods of New Alpha Power-Transformed Pareto Model with Applications in Insurance

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.

Some Properties of the Cosine Lomax Distribution with Applications

This paper introduces a new trigonometric distribution, named the Cosine Lomax (CLM) distribution. This distribution is a combination of the Lomax distribution and the Cosine-G family of distributions. Among the many mathematical moments, moment-generating function, incomplete moments, and the quantile function. We try to determine the model parameters using the maximum likelihood estimation method. Simulation studies evaluate the effectiveness of maximum likelihood estimators using bias and root mean square error. We applied the CLM distribution to two real-world datasets and tested for consistency using the Akaike information criterion, the consistent AIC, the Hannan-Quinn information criterion, the Bayesian information criterion, the Kolmogorov-Smirnov p-value, Cramer Von-Mises, and Andersen-Darling. The CLM model fared better when compared to the following distributions: Lomax, Inverse Lomax, Inverse Weibull, Burr Type X, Rayleigh, and Exponential, as well as measures of data set fit.

Advancing oncological practice with innovative cancer data analytics: A new exponential-generated class of distributions

Traditional predictive modeling techniques have significantly influenced the analysis of survival times and predictive markers in oncology. However, these models often do not fully address the complexities of cancer data, leading to a noticeable gap in accurately modeling both cancer survival and mortality. The aim of this study is to show a model that offers the best fit for cancer mortality and survival data, thereby improving treatment strategies and patient prognoses. I propose the a New Exponential-Weibull (NEWE) distribution within the New Exponential-Generated (NE-G) class of distributions to enhance oncological analytics with greater accuracy and comprehensiveness. An empirical analysis of Brazilian cancer mortality data is conducted., This data set covers children, head and neck, and cervical cancer. Concurrently, survival time-to-event data for bladder and advanced lung cancers patients are assessed to evaluate the model’s effectiveness. Based on standard metrics, extensive simulation experiments show the Maximum Product of Spacing Estimator as the best of seven-point estimation techniques. The NEWE distribution shows superior modeling capabilities, surpassing traditional models with lower values of Log-likelihood, Cramer-von Mises, and Anderson-Darling and higher Kolmogorov-Smirnov (KS) p-values. The study also discerns the most fitting estimators for distinct types of cancer mortality and survival data. This includes the Right Tail Anderson-Darling for child cancer deaths, the Maximum Product Spacing for head and neck cancer deaths, the Least Squares for cervical cancer deaths, the Weighted Least Squares for bladder cancer survival, and the Anderson-Darling for advanced lung cancer deaths. This shows that the NEWE distribution can be used in a number of different cancers settings. The development and implementation of the NEWE distribution marks a significant advancement in oncological modeling. By analyzing both cancer mortality and survival data with enhanced accuracy and flexibility, this novel approach surpasses traditional models, offering deeper insights into cancer progression and treatment outcomes. As a result, the NEWE distribution equips healthcare professionals with a powerful tool for improving clinical decisions, leading to better prognostic assessments and patient care in cancer treatment.

Comparison of different estimation methods for the inverse power perk distribution with applications in engineering and actuarial sciences

Introducing the Inverse Power Perk distribution, this paper presents a versatile probability distribution designed to model positively skewed data with unprecedented flexibility. Building upon the Perk distribution, it accommodates a wide range of shapes including right-skewed, J-shaped, reversed J-shaped, and nearly symmetric densities, as well as hazard rates exhibiting various patterns of increase and decrease. The paper delves into the mathematical properties of this novel distribution and offers a comprehensive overview of estimation techniques, including maximum likelihood estimators, ordinary least square estimators, percentile-based estimators, maximum product of spacing estimators, Cramer-von Mises, weighted least squares estimators, and Anderson-Darling estimators. To assess the performance of these estimation methods across different sample sizes, Monte Carlo simulations are conducted. Through comparisons of average absolute error and mean squared error, the efficacy of each estimator is evaluated, shedding light on their suitability for both small and large samples. In a practical application, three real datasets, including insurance data, are employed to demonstrate the versatility of the current model, when comparing to existing alternatives. The IPP distribution offers significant advantages over traditional distributions, particularly in its superior ability to model tail risks, making it an invaluable tool for practitioners dealing with extreme values and rare events. Its computational efficiency further sets it apart, enabling more robust and faster analysis in large-scale datasets.This empirical analysis further underscores the utility and adaptability of the Inverse Power Perk model in capturing the nuances of diverse datasets, thereby offering valuable insights for practitioners in various fields.

A New Goodness of Fit Test for Complete or Type II Right Censored Samples

This study proposes a new goodness-of-fit test based on the empirical distribution function for complete or type II right-censored random samples, which are drawn from either the exponential or log-normal distributions. Some simulation studies were conducted to compare the newly proposed test with some of the well-known goodness-of-fit tests, such as Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, in terms of power over various sample sizes and censoring rates. The simulation results show that the newly proposed goodness of fit test generally seems to perform well compared to the other goodness of fit tests considered. In addition, the newly proposed test and the other goodness of fit tests are illustrated by applying them to some real data sets obtained from the relevant literature.

Different Estimation Methods for A New Extension Three Parameter Log-Logistic Distribution with Applications

This article presents a new extension of the three-parameter log-logistic distribution, the so-called heavy-tailed log-logistic (HTLL) distribution. Some important mathematical properties of the new HTLL distribution are calculated. In addition, some numerical results of moments for the HTLL distribution are calculated. Extensive simulations were performed to investigate the estimation of the model parameters using many established approaches, including maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cramer-von Mises (CVM), Anderson-Darling (AD), and right-tail Anderson-Darling (RTAD). The simulation results show that the AD approach has the highest efficiency among these approaches. The usefulness of the newly proposed model is demonstrated by analyzing two real data sets.

Estimating the survival function Maximum Likelihood and Cramér-Von Mises Method use of amixture distribution weibull and ailamujia with apractical application

Tow failure distributions were mixed ,weibull distribution and ailamujia distribution it's called weibull –ailamujia distribution which consists of four features, the two distributions were mixed by adding a mixing parameter ,the mixture of two distributions would be more efficient ,and representative of the data than the single distributions. A group of statistical properties of the mixture distribution were studied , such as the probability function ,the survival function and the failure rate function .classical estimation method were used to estimate the parameters of the mixture distribution, which are maximum likelihood of method ,the cramer –von mises method ,The method were compared using monte carlo simulations real data were taken regarding drug –resistant tuberculosis (TB) Multi Drug Resistance(MDR) methods were compared using the MSE statistical criterion ,and the result should a preference for the method cramer-von mises for having the lowest MSE

Identifying the Probability Distribution of Exchange Rates in Sri Lanka

The exchange rate is one of the main components that represents the status of a country’s economic condition. This study mainly focuses on identifying an appropriate distribution that can capture the asymmetric behaviour of important currency exchange rates related to Sri Lanka. The true behaviour of the exchange rates of USD, EURO, JPY, AUD, GBP, CHF, SGD and CAD in terms of LKR was determined using flexible distributions of generalised lambda distribution (GLD), Normal Inverse Gaussian and Skew-Normal. The parameter estimation was carried out by maximum likelihood estimation (MLE), while for GLD, few more parameter estimation techniques were applied. To understand how well the fitted distributions identify the real behaviour of data, we conducted the goodness-of-fit (GOF) tests. The results from Cramer–Von Mises (CvM) and Anderson–Darling (AD) GOF tests pointed out that the exchange rates data follow a GLD with the parameter estimation of maximum product of spacings (MPS). Further, plots of histograms with theoretical densities, cumulative distribution functions (CDFs) with empirical CDF and Quantile–Quantile plots illustrated the same idea. This study presented the findings based on different suitable parameter estimation techniques and this study is the first investigation on the distribution identification of exchange rates in Sri Lanka. JEL Codes: C12,C13,G10

Modified Exponential Power distribution with properties and applications

We have developed the Modified Exponential power distribution, a new and adaptable probability distribution, in this work. An additional shape parameter is added to the exponential power distribution to create this distribution. Numerous statistical properties of suggested model are derived and analyzed. Cramer-Von-Mises (CVME), maximum likelihood (MLE), and least-squares (LSE) are used to estimate the model's parameters. P-P and Q-Q charts are used to assess the validity of the model. Several information criteria are applied in model comparisons, including the Bayesian Information Criterion (BIC), the Hannan-Quinn Information Criterion (HQIC), the Corrected Akaike Information Criterion (CAIC), and the Akaike Information Criterion (AIC). These criteria help determine the best model by balancing goodness-of-fit with model complexity. Test statistics, together with their corresponding p-values, are also utilized to evaluate the recommended model's goodness of fit. These tests consist of the Kolmogorov-Smirnov (KS), Cramer-Von Mises (CVM), and Anderson-Darling (An) tests. R programming is used for the dataset analysis and visualization.

Simulating phenomena with exponentiated trigonometric distributions: a comparative study of estimation methods and real-world applications

Recent research has highlighted the statistical significance and usefulness of trigonometric distribution models for simulating a variety of phenomena. A new set of distributions generated by exponentiated cosine and tangent functions has been introduced. Consequently, two families of distributions called the exponentiated cosine and tan Stacy distributions are derived. Some vital statistical and reliability characteristics are studied. The finite sample characteristics of parameter estimations are compared to the exponentiated cosine and tan distribution generated by four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Cramer–von Mises. The methodologies are evaluated using simulation studies. Finally, the practical applications of the proposed trigonometric versions of the Stacy model are examined and applied on two lifetime reliability engineering datasets and another lifetime medical dataset concerning bladder cancer data. These real applications serve to highlight the effectiveness and adaptability of this innovative families within the respective fields compared with other lifetime well-known distribution models.

On Power Chris-Jerry Distribution: Properties and Parameter Estimation Methods

In this study, we introduce the "Power Chris-Jerry" distribution, conducting a comprehensive analysis of its fundamental mathematical characteristics and an extensive exploration of various crucial aspects. These encompass investigations into its mode, quantile function, moments, coefficient of skewness, kurtosis, moment generating function, stochastic ordering, distribution of order statistics, reliability analysis, and mean past lifetime. Furthermore, we provide an in-depth assessment of four distinct parameter estimation methodologies: maximum likelihood estimation (MLE), Least Squares (LS), maximum product spacing method (MPS), and the Method of Cram`er-von-Mises (CVM). Our investigation uncovers a consistent pattern wherein the MLE, LS, and CVM approaches consistently yield underestimated parameter values. Intriguingly, we observe a consistent trend of decreasing Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and BIAS across all estimation techniques as sample sizes increase. Remarkably, our simulation results consistently favor the Maximum Product Spacing (MPS) method, highlighting its superiority in generating estimates with smaller MSE values across a broad spectrum of parameter values and sample sizes. These findings emphasize the robustness and dependability of the MPS estimator, offering valuable insights and practical guidance for both practitioners and researchers engaged in probability distribution modeling.

Performance evaluation of estimators in the presence of outliers or omitted predictors: a study on the Poisson-Exponential regression model

The Poisson regression model is vulnerable for overdispersion in the data when estimating model parameters and their standard errors. Overdispersion may occur due to outliers in the data and/or removal of important predictors from the model. This paper employs a regression model that can be used to better cope with outliers and omitted predictor bias in count data compared to the Poisson regression model, namely the Poisson exponential (PE) model which is a reparameterization of the geometric regression model. Along with investigating the distributional properties of the PE distribution, the usual maximum likelihood (ML-I), maximum likelihood with Expectation-maximization algorithm (ML-II), least-square (LS), weighted least-square (WLS), least-absolute deviation (LAD), weighted least-absolute deviation (WLAD), and Cramer-von mises (CVM) estimation methods are utilized in the context of the PE regression model. The performance of these estimation methods with the PE regression model are inspected through two comprehensive simulation studies. The first is conducted on data sets with and without outliers. The second investigates the performance of the estimation methods for the PE regression model with and without omitted predictors. Two real-life applications illustrate the applicability of the PE regression model with the estimation methods for these two situations.

Power unit Burr-XII distribution: Statistical inference with applications

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution.

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the proposed model is tested using Kolmogrov-Smirnov (KS), Cramer-Von Mises (CVM) and Anderson-Darling (An) test statistics along with respective p-values. All the analysis of the study is performed by using R programming.

Distribution of squared sum of products of independent Nakagami-m random variables

The need for the distribution of combination of random variables (RVs) arises in many areas of sciences and engineering. In this paper, closed-form approximations for the distribution of squared sum of products of independent Nakagami-m RVs are derived. Three different approaches (central limit theorem, Edgeworth expansion, and a one-term gamma approximation) are considered. The Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises statistics are used as a quantitative metrics to compare the derived distribution forms with the empirical distribution obtained from a simulation study. Furthermore, an application for the derived distributions in wireless communication field is presented. As a result, it is shown that the most accurate and simplest closed-form expression is the one obtained by a one-term gamma approximation.

Unit-Weibull Distribution: Different Method of Estimations

Recently, the unit-Weibull (UW) distribution is used quite effectively in analyzing lifetime data. The main goal of this article is to investigate the performance of seven estimation methods, namely maximum likelihood (ML), least square (LS), weighted least square (WLS), Anderson-Darling (AD), right-tail Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) for parameter estimation. An extensive Monte Carlo simulation study is considered to compare the performances of these methods through biases and mean square errors (MSEs). The numerical results show that the PCE estimator has significantly smaller MSE value for different sample sizes and parameter values in most cases. In addition, the ML and LS estimators have lower bias values than the other estimators in general. Finally, a real data set is presented for illustrative purposes.

The odd lindley power rayleigh distribution: properties, classical and bayesian estimation with applications

In this paper, we propose and investigate the odd Lindley Power Rayleigh (OLPR) distribution, which is derived by combining the odd Lindley-G family and power Rayleigh distribution. The proposed distribution, which is comparable to the Lindley distribution, Rayleigh distribution and other Rayleigh generalizations have the desirable attribute of allowing greater flexibility than some of its well known extensions. A comprehensive account of the mathematical and statistical properties along with the estimation of parameters using classical and Bayesian estimation methodologies is presented. An extensive simulation study is carried out to assess the behaviour of estimators based on their biases and mean square errors. Finally, we consider two practical real-life applications, we observe that the proposed model outperforms other competing models using the Akaike information criterion (AIC), the Bayesian information criterion (BIC), Anderson-Darling (A*), Cramer-von Mises (W*) and other goodness-of-fit measures.

Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference

ABSTRACT Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time’s data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.

Assessment of the variability of the I-V characteristic of HfO2-based resistive switching devices and its simulation using the quasi-static memdiode model

Variability of the conduction characteristics of filamentary-type resistive switching devices or resistive RAMs (RRAMs) is a hot research topic both in academia and industry because it is currently considered one of the major showstoppers for the successful development and application of this technology. In this work, we thoroughly investigate the statistics of the cycle-to-cycle (C2C) variability observed in the experimental current–voltage (I-V) curves of HfO2-based memristive structures using the fitdistrplus package for the R language. This exploratory analysis allows us to identify which parametric probability distributions are the most suitable candidates for describing our data. This study involves graphical tools such as the density, skewness-kurtosis (S-K), and quantile–quantile (Q-Q) plots. The analysis is completed with the aid of goodness-of-fit statistics (Kolmogorov-Smirnov, Cramer-von Mises, Anderson-Darling) and criteria (Akaike’s and Bayesian). The selected distributions are incorporated into the SPICE script of the quasi-static memdiode model for resistive switching devices and used for simulating uncorrelated C2C variability. Finally, a one-way sensitivity analysis is carried out in order to test the impact of the model parameters variation in the output characteristics of the device.