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In this paper, a new approach is presented to fit a fuzzy regression model with the fuzzy coefficients when the explanatory variables and the response variable are as fuzzy numbers. In this approach, a nonlinear function is introduced to predict the response variables based on the kernel function. To estimate the parameters of regression model, the objective function is calculated using the quantile loss function on fuzzy numbers. To evaluate the goodness of fit of the optimal quantile fuzzy regression models, two indices are introduced using the similarity measures. Based on the presented results, the proposed fuzzy regression models have the perfect performances on the original data and also in the presences of different types of outliers. [ABSTRACT FROM AUTHOR]

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models—specifically the original performance equation (PE‐1) and its generalized counterpart (GPE‐1)—to fit rotated and right‐shifted Lorenz curves. Notably, another potential performance equation (PE‐2), capable of generating similar curves to PE‐1, has been overlooked and not systematically compared with PE‐1 and GPE‐1. Furthermore, PE‐2 has been extended into a generalized version (GPE‐2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root‐mean‐square errors of all four performance models were consistently smaller than 0.05. Paired t‐tests indicated that GPE‐1 exhibited the lowest root‐mean‐square error and Akaike information criterion value among the four performance equations. However, PE‐2 gave the best close‐to‐linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution. [ABSTRACT FROM AUTHOR]

The goodness of fit (GOF) test is an intensely crucial and meaningful issue in scientific research because it is widely applied in sciences such as statistics, applied mathematics, economics, finance, engineering, and so on. To the extent of this article, we first revisit the GOF test for the logistic model, and then we propose the GOF test for the zero-inflated Bernoulli (ZIBer) model. We seek to establish Karl Pearson's chi-square test and unweighted residual sum of square test for this model. Afterward, we demonstrate that both tests have an asymptotic normal distribution with a mean and standard deviation that they derived. Simulation studies and an actual data set are also studied to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study is to introduce and analyze the Topp-Leone Kumaraswamy Fréchet (TLKFr) distribution a new probability distribution model. This model extends the classical Fréchet distribution by introducing three additional positive shape parameters to enhance flexibility and robustness. Material and Methods: The novel distribution is based on the Topp-Leone Kumaraswamy generalized distribution family, incorporating three shape parameters. This foundation allows for the derivation of both the cumulative distribution function and probability density function for the new distribution. The study also extensively explores the mathematical properties of this distribution, including the survival, hazard, and quantile functions. Parameter estimation is conducted using the maximum likelihood estimation (MLE) technique. Results: The study introduces the TLKFr distribution, providing mathematical expressions for key statistical measures. Parameters were estimated using MLE technique. Plots illustrate the distribution's characteristics, showing positive skewness and reliable survival analysis predictions. Simulation analysis indicates decreasing bias and root mean square error (RMSE) with larger sample sizes, emphasizing reliability. Application to two real-life datasets, demonstrates the TLKFr distribution consistently outperforming rival models, supported by goodness-of-fit statistics. Conclusion: The study introduces and analyzes the TLKFr distribution, enhancing the traditional Fréchet distribution with three additional shape parameters. Mathematical characteristics are explored, employing MLE for parameter estimation. A simulation study underscores the distribution's strong reliability, evident in decreasing bias and RMSE with increasing sample size. When tested with real datasets, the TLKFr distribution outperforms alternative models, highlighting its significance in representing real-world phenomena and validating its applicability to the two datasets examined in this study. [ABSTRACT FROM AUTHOR]

In data analysis, we cannot expect the data under study to always follow a symmetric probability distribution; they can have a skewed probability distribution. Modeling skewed data is a challenging task for data scientists. A mixture of probability distributions is a better option for modelling skewed data. In this study, we generated a few mixtures of probability distributions using the exponential as the first fixed component and Gompertz, Lindley, and log-normal distributions as the second component for modelling skewed data. We also examined the characteristics of mixed probability distributions. The maximum likelihood method was used to estimate the unknown parameters. As a result, all three mixture models have a right-skewed pattern, which provides a better fit than existing distributions. Finally, we used real-time datasets to model skewed data. [ABSTRACT FROM AUTHOR]

Replication provides a confrontation of psychological theory, not only in experimental research, but also in model-based research. Goodness of fit (GOF) of the original model to the replication data is routinely provided as meaningful evidence of replication. We demonstrate, however, that GOF obscures important differences between the original and replication studies. As an alternative, we present Bayesian prior predictive similarity checking: a tool for rigorously evaluating the degree to which the data patterns and parameter estimates of a model replication study resemble those of the original study. We apply this method to original and replication data from the National Comorbidity Survey. Both data sets yielded excellent GOF, but the similarity checks often failed to support close or approximate empirical replication, especially when examining covariance patterns and indicator thresholds. We conclude with recommendations for applied research, including registered reports of model-based research, and provide extensive annotated R code to facilitate future applications of prior predictive similarity checking. [ABSTRACT FROM AUTHOR]

Models for forecasting various ecosystem properties have great potential that comes with a need for model validation. Before we can perform such validation, we need to define what it means for the model to perform well, which depends on the question being asked. Often, it seems easy to ignore the model question and take a standard well-known error measure for comparing the model to the available data. The question is whether this practice is adequate. Here, we defined different types of model-data mismatches that may be more or less relevant to different types of questions. We show that error measures differ in their sensitivity to the type of mismatch and robustness to sparse and noisy data. The results imply that a careful selection of error measures, using a clearly defined ecological question as a starting point, is vital to proper model evaluation. While we present our results as generally applicable to the validation of any type of forecasting model, we also illustrate them using cyanobacterial bloom modelling as a detailed example of a case where different questions could be asked of the same model. • We show the need for a well-defined model question before model evaluation. • Error measures differ with respect to the question they ask the model. • Error measures differ in their robustness to sparse and noisy data. • The choice of error measure can strongly affect the model training/validation outcome. • The above is illustrated with a detailed example of cyanobacterial bloom modelling. [ABSTRACT FROM AUTHOR]