scholarly journals An α-Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1400
Author(s):  
Talha Arslan
Keyword(s):  
Goodness Of Fit ◽  
Rate Function ◽  
Information Criteria ◽  
Environmental Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Fit Statistics ◽  
Bathtub Shape ◽  
Comparison Results ◽  
Environmental Events

Modeling environmental data plays a crucial role in explaining environmental phenomena. In some cases, well-known distributions, e.g., Weibull, inverse Weibull, and Gumbel distributions, cannot model environmental events adequately. Therefore, many authors tried to find new statistical distributions to represent environmental phenomena more accurately. In this paper, an α-monotone generalized log-Moyal (α-GlogM) distribution is introduced and some statistical properties such as cumulative distribution function, hazard rate function (hrf), scale-mixture representation, and moments are derived. The hrf of the α-GlogM distribution can form a variety of shapes including the bathtub shape. The α-GlogM distribution converges to generalized half-normal (GHN) and inverse GHN distributions. It reduces to slash GHN and α-monotone inverse GHN distributions for certain parameter settings. Environmental data sets are used to show implementations of the α-GlogM distribution and also to compare its modeling performance with its rivals. The comparisons are carried out using well-known information criteria and goodness-of-fit statistics. The comparison results show that the α-GlogM distribution is preferable over its rivals in terms of the modeling capability.

scholarly journals Goodness–of–fit statistics and CMB data sets

2003 ◽  
Vol 410 (1) ◽  
pp. 11-16 ◽  
Author(s):  
M. Douspis ◽  
J. G. Bartlett ◽  
A. Blanchard
Keyword(s):  
Goodness Of Fit ◽  
Data Sets ◽  
Fit Statistics

scholarly journals The Iwok-Nwikpe Distribution: Statistical Properties and Its Application

2021 ◽  
pp. 35-45
Author(s):  
Iwok Iberedem Aniefiok ◽  
Barinaadaa John Nwikpe
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Medical Science ◽  
Mathematical Expression ◽  
Real Data ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets

In this paper, a new continuous probability distribution named Iwok-Nwikpe distribution is proposed. Some essential statistical properties of the proposed probability distribution have been derived. The graphs of the survival function, probability density function (p.d.f) and cumulative distribution function (c.d.f) were plotted at different values of the parameter. The mathematical expression for the moment generating function (mgf) was derived. Consequently, the first three crude moments were obtained; the distribution of order statistics, the second and third moments corrected for the mean have also been derived. The parameter of the Iwok-Nwikpe distribution was estimated by means of maximum likelihood technique. To establish the goodness of fit of the Iwok-Nwikpe distribution, three real data sets from engineering and medical science were fitted to the distribution. Findings of the study revealed that the Iwok-Nwikpe distribution performed better than the one parameter exponential distribution and other competing models used for the study.

scholarly journals Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets

2019 ◽  
Author(s):  
Jan Graffelman
Keyword(s):  
Multidimensional Scaling ◽  
Goodness Of Fit ◽  
Large Data ◽  
Distance Matrix ◽  
Large Data Sets ◽  
Data Sets ◽  
Fit Statistics ◽  
Metric Multidimensional Scaling ◽  
Scientific Disciplines ◽  
Almost All

AbstractMetric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the over-all goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise good-ness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasising the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown.

scholarly journals Investigation of the Effects of Silage Type, Silage Consumption, Birth Type and Birth Weight on Live Weight in Kıvırcık Lambs With MARS and Bagging MARS Algorithms.

2021 ◽  
Author(s):  
Ömer ŞENGÜL ◽  
Şenol Çelik ◽  
İbrahim AK
Keyword(s):  
Birth Weight ◽  
Goodness Of Fit ◽  
Live Weight ◽  
Information Criteria ◽  
Corn Silage ◽  
Multivariate Adaptive Regression Splines ◽  
Percentage Error ◽  
Absolute Deviation ◽  
Fit Statistics ◽  
Birth Type

Abstract This study was carried out to determine the effect of silage type, silage consumption, birth type (single or twin) and birth weight on live weight at the end of fattening in Kıvırcık lambs. In the experiment, 40 male Kıvırcık lambs aged 2.5-3 months were used and the animals were fattened for 56 days. During the fattening period, the lambs fed with 5 different types of silage (100% sunflower silage, 75% sunflower + 25% corn silage, 50% sunflower + 50% corn silage, 25% sunflower + 75% corn silage, 100% corn silage) pure and mixed in different proportions and concentrate feed. Data on fattening results were analyzed with MARS and Bagging MARS algorithms. The main objective of this research is to predict live weight of lambs using Multivariate Adaptive Regression Splines (MARS) and Bagging MARS algorithms as a nonparametric regression technique. Live weight value was modeled based on factors such as birth type, birth weight, silage type and silage consumption. Correlation coefficient (r), determination coefficient (R2), Adjust R2, Root-mean-square error (RMSE), standard deviation ratio (SD ratio), mean absolute percentage error (MAPE), mean absolute deviation (MAD), and Akaike Information Criteria (AIC) values of MARS algorithm predicting live weight were as follows: 0.9986, 0.997, 0.977, 0.142, 0.052, 0.2389, 0.086 and -88 respectively. Like statistics for Bagging MARS algorithm were 0.754, 0.556, 0.453, 1.8, 0.666, 3.96, 1.47 and 115 respectively. It was observed that MARS and Bagging MARS algorithms have revealed correct results according to goodness of fit statistics. However, it has been revealed that MARS algorithm gives better results in live weight modeling.

scholarly journals An Extended Pranav Distribution

2019 ◽  
pp. 1-15
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan ◽  
U. C. Orumie
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Maximum Likelihood Estimates ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Rate Functions ◽  
New Distribution

In this study, we proposed a generalization of the Pranav distribution by Shukla (2018). This new distribution called an extended Pranav distribution is obtained using the exponentiation method. The statistical characteristics of this new distribution such as the moments, moment generating function, reliability function, hazard function, Rényi entropy and order statistics are derived. The graphical illustrations of the shapes of the probability density function, the cumulative distribution function, and hazard rate functions are provided. The maximum likelihood estimates of the parameters were obtained and finally, we examine the performance of this new distribution using some real-life data sets to show its flexibility and better goodness of fit as compared with other distributions.

scholarly journals The gamma exponentiated exponential-Weibull distribution

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3159-3170 ◽  
Author(s):  
Tibor Pogány ◽  
Abdus Saboor
Keyword(s):  
Biological Sciences ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Data Sets ◽  
Fit Statistics ◽  
Positive Data ◽  
Special Cases ◽  
Likelihood Approach ◽  
Anderson Darling ◽  
Von Mises

Anewfour-parameter model called the gamma-exponentiated exponential-Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson-Darling and Cram?r-von Mises goodness-of-fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

scholarly journals A New Compound Gamma and Lindley Distribution with Application to Failure Data

2019 ◽  
Vol 48 (3) ◽  
pp. 54-75
Author(s):  
Mousa Abdi ◽  
Akbar Asgharzadeh ◽  
Hassan S. Bakouch ◽  
Zahra Alipour
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Stochastic Order ◽  
Rate Function ◽  
Estimation Methods ◽  
Strength Parameter ◽  
Data Sets ◽  
Failure Data ◽  
Distribution Parameters ◽  
Stochastic Order Relations

 In this paper, we propose a new lifetime distribution by compounding the gamma and Lindley distributions. Construction of it can be interpreted in the viewpoint of the reliability analysis and Bayesian inference. Moreover, the distribution has decreasing and unimodal hazard rate shapes. Several properties of the distribution are obtained, involving characteristics of the (reverse) hazard rate function, quantiles, moments, extreme order statistics and some stochastic order relations. Estimating the distribution parameters is discussed by some estimation methods and their performance is evaluated by a simulation study. Also, estimation of the stress-strength parameter is investigated. Usefulness of the distribution among other models is illustrated by fitting two failure data sets and using some goodness-of-fit measures.

scholarly journals Inverse Power Akash Probability Distribution with Applications

2020 ◽  
pp. 1-32
Author(s):  
Samuel U. Enogwe ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Inverse Power ◽  
Data Sets ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Heavy Tailed

This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.

scholarly journals Parameter Estimation Techniques Based on Optimizing Goodness-of-Fit Statistics for Structural Reliability

1993 ◽  
Author(s):  
Alois Starlinger ◽  
Stephen F. Duffy ◽  
Joseph L. Palko
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Structural Reliability ◽  
Empirical Distribution ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Weibull Parameters ◽  
Fit Statistics ◽  
Failure Data

Abstract New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell’s numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper’s nonlinear regression algorithm.

Bootstrap Analysis

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Real Data ◽  
Confidence Regions ◽  
Confidence Bands ◽  
Cumulative Distribution ◽  
Attractive Alternative ◽  
Bootstrap Analysis ◽  
Parametric Bootstrapping ◽  
Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

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