Browsing by Author "Arslan, Talha"

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Alpha Power Inverted Kumaraswamy Distribution: Definition, Different Estimation Methods and Application
(Univ Punjab, 2022) Bagci, Kubra; Erdogan, Necati; Arslan, Talha; Celik, H. Eray
In this study, an alpha power inverted Kumaraswamy distribution having three shape parameters is obtained by applying the alpha power transformation to the inverted Kumaraswamy distribution. Then, its survival and hazard rate functions are expressed in closed forms. Some of its submodels and limiting cases are provided as well. Its parameters are estimated by using the maximum likelihood, maximum product of spacings, and least squares methods. A Monte-Carlo simulation study is conducted to show the performances of the considered estimation methods. An application to a real data set including values of breaking stress of carbon fibers is provided to illustrate an implementation of the proposed distribution and its modeling capability. The results show that alpha power inverted Kumaraswamy distribution can be an alternative to the its rivals.
Estimation of the Location and Scale Parameters of Moyal Distribution
(Turkic World Mathematical Soc, 2020) Arslan, Talha; Acitas, Sukru; Senoglu, Birdal
In this study, we estimate the parameters of the Moyal distribution by using well-known and widely-used maximum likelihood (ML) and method of moments (MoM) methodologies. The ML estimators of the location and scale parameters of the Moyal distribution cannot be obtained in closed forms therefore iterative methods should be utilized. To make the study complete, modifed ML (MML) estimators for the location and the scale parameters of the Moyal distribution are also derived. The MML estimators are in closed forms and asymptotically equivalent to the ML estimators. Efficiencies of the MML estimators are compared with their ML and MoM counterparts using Monte-Carlo (MC) simulation study. Results of the simulation study show that the ML estimators are more efficient than the MML and MoM estimators for small sample sizes. However when the sample size increases performances of the ML and MML estimators are almost same in terms of the Defficiency (Def) criterion as expected. At the end of the study, a real data set is used to show the implementation of the methodology developed in this paper.
Inverted Kumarswamy Distribution for Modeling the Wind Speed Data: Lake Van, Turkey
(Pergamon-elsevier Science Ltd, 2021) Bagci, Kubra; Arslan, Talha; Celik, H. Eray
In calculating the wind energy potential of a region, some important points such as determining the distribution used to model wind speeds and estimating the parameters of the distribution accurately should be considered. Many different distributions have been proposed in wind energy literature over the years. In this paper, some of these studies are reviewed. Then, Inverted Kumaraswamy (IKum) distribution is used for the first time to model wind speed data as an alternative to the well-accepted Weibull distribution. Maximum Likelihood, Least Squares, and Maximum Product of Spacing methodologies are employed in estimating the parameters of the IKum distribution. A Monte Carlo simulation study is conducted for comparing the efficiencies of these methods. The wind speed data sets considered in this study include wind speeds from 6 stations located around Lake Van in Turkey. Modeling performances of the Weibull and IKum distributions are evaluated with the well-known goodness-of-fit criteria and power density error values. Results show that the IKum distribution can be considered as an alternative to the well-accepted Weibull distribution.
Modified Minimum Distance Estimators: Definition, Properties and Applications
(Springer Heidelberg, 2022) Arslan, Talha; Acitas, Sukru; Senoglu, Birdal
Estimating the location and scale parameters of a distribution is one of themost crucial issues in Statistics. Therefore, various estimators are proposed for estimating them, such as maximum likelihood, method of moments and minimum distance (e.g. Cramervon Mises-CvM and Anderson Darling-AD), etc. However, in most of the cases, estimators of the location parameter mu and scale parameter s cannot be obtained in closed forms because of the nonlinear function(s) included in the corresponding estimating equations. Therefore, numerical methods are used to obtain the estimates of these parameters. However, they may have some drawbacks such as multiple roots, wrong convergency, and non-convergency of iterations. In this study, we adopt the idea of Tiku (Biometrika 54:155-165, 1967) into the CvM and AD methodologies with the intent of eliminating the aforementioned difficulties and obtaining closed form estimators of the parameters mu and s. Resulting estimators are called as modified CvM (MCvM) and modified AD (MAD), respectively. Proposed estimators are expressed as functions of sample observations and thus their calculations are straightforward. This property also allows us to avoid computational cost of iteration. A Monte-Carlo simulation study is conducted to compare the efficiencies of the CvM and AD estimators with their modified counterparts, i.e. the MCvM and MAD, for the normal, extreme value and Weibull distributions for an illustration. Real data sets are used to show the implementation of the proposed estimation methodologies.
Oestrogen and Progesterone Concentrations in Intrapartum Cows With Insufficient Cervix Dilation
(Wiley, 2024) Sendag, Sait; Koca, Davut; Arslan, Talha; Schuler, Gerhard; Wehrend, Axel
The cervix is an important organ that has to dilate sufficiently at delivery to allow the foetus to transition to extrauterine life. Insufficient dilatation of the cervix (IDC) is a frequent cause of dystocia in cattle. The mechanisms underlying cervical opening and the pathogenesis of IDC are still widely unclear. Systematic studies on the relationship between IDC and steroid hormones have been limited and have yielded inconsistent findings. This study aimed to measure oestrogen and progesterone (P4) concentrations in intrapartum cows presented with dystocia due to IDC and in a comparison (C) group of cows with eutocic delivery. Before any obstetrical procedures, and right after the initial evaluation, blood samples were taken from IDC and C animals. Concentrations of P4, oestradiol-17 beta (E2), free total oestrogens (FTE) and conjugated total oestrogens (CTE) were measured by established radioimmunoassays. Concentrations of P4 (p = .538), FTE (p = .065) and CTE (p = .605) were not statistically different between C and IDC groups. However, E2 levels in group C were significantly lower when compared to those in the IDC group (p = .013), which is inconsistent with the function of oestrogens in cervical dilatation. The correlation analysis demonstrated significant positive correlations between the pairs P4 versus FTE, P4 versus E2 and FTE versus E2 in group C and between the pair FTE versus E2 in group IDC. In conclusion, the results suggest that local activities of steroids relevant to the aetiology of IDC are not reflected by concentrations in the systemic circulation or that other factors are clearly more important.
Parameter Estimation for Thetwo-Parameter Maxwell Distribution Under Complete and Censored Samples
(inst Nacional Estatistica-ine, 2021) Arslan, Talha; Acitas, Sukru; Senoglu, Birdal
The Maxwell distribution is one of the basic distributions in Physics besides being popular in Statistics for modeling lifetime data. This paper considers the parameter estimation of the Maxwell distribution via modified maximum likelihood (MML) methodology for both complete and censored samples. The MML estimators for the location and scale parameters of the Maxwell distribution have explicit forms and they are robust against the plausible deviations from the assumed model. A Monte Carlo simulation study is conducted to compare the performances of the MML estimators with the corresponding maximum likelihood (ML), least squares (LS) and method of moments (MoM) estimators.
Slash Maxwell Distribution: Definition, Modified Maximum Likelihood Estimation and Applications
(Gazi Univ, 2020) Acitas, Sukru; Arslan, Talha; Senoglu, Birdal
In this study slash Maxwell (SM) distribution, defined as a ratio of a Maxwell random variate to a power of an independent uniform random variate, is introduced. Its stochastic representation and some distributional properties such as moments, skewness and kurtosis measures are provided. The maximum likelihood (ML) method is used for estimating the unknown parameters. However, closed forms of the ML estimators cannot be obtained since the likelihood equations include nonlinear functions of the unknown parameters. We therefore use Tiku's (1967,1968) modified maximum likelihood (MML) methodology which allows to obtain explicit forms of the estimators. Some asymptotic properties of the MML estimators are derived. A Monte-Carlo simulation study is also carried out to compare the performances of the ML and MML estimators. Two data sets taken from the literature are modelled using the SM distribution in application part of the study.
A Versatile Model for Lifetime of a Component Under Stress
(Nature Portfolio, 2023) Almuhayfith, Fatimah E.; Arslan, Talha; Bakouch, Hassan S.; Alnaghmosh, Aminh M.
In this study, a versatile model, called alpha-monotone inverse Weibull distribution ( alpha IW), for lifetime of a component under stress is introduced by using the alpha-monotone concept. The alpha IW distribution is also expressed as a scale-mixture between the inverse Weibull distribution and uniform distribution on (0, 1). The alpha IW distribution includes alpha-monotone inverse exponential and alpha-monotone inverse Rayleigh distributions as submodels and converenges to the inverse Weibull, inverse exponential, and inverse Rayleigh distributions as limiting cases. Also, slash Weibull, slash Rayleigh, and slash exponential distribuitons can be obtained under certain variable transformation and parameter settings. The alpha IW distribution is characterized by its hazard rate function and characterizing conditions are provided as well. Maximum likelihood, maximum product of spacing, and least squares methods are used to estimate distribution parameters. A Monte-Carlo simulation study is conducted to compare the efficiencies of the considered estimation methods. In the application part, two practical data sets, Kevlar 49/epoxy and Kevlar 373/epoxy, are modeled via the alpha IW distribution. Modeling performance of the alpha IW distribution is compared with its rivals by means of some well-known goodness-of-fit statistics and results show that alpha IW distribution performs better modeling than them. Results of comparison also indicate that obtaining the alpha IW distribution by using the alpha-monotone concept is cost effective since the new shape parameter added to the distribution by using the alpha-monotone concept significantly increases the modeling capability of the IW distribution. As a result of this study, it is shown that the alpha IW distribution can be an alternative to the well-known and recently-introduced distributions for modeling purposes.
An Α-Monotone Generalized Log-Moyal Distribution With Applications To Environmental Data
(Mdpi, 2021) Arslan, Talha
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 alpha-monotone generalized log-Moyal (alpha-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 alpha-GlogM distribution can form a variety of shapes including the bathtub shape. The alpha-GlogM distribution converges to generalized half-normal (GHN) and inverse GHN distributions. It reduces to slash GHN and alpha-monotone inverse GHN distributions for certain parameter settings. Environmental data sets are used to show implementations of the alpha-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 alpha-GlogM distribution is preferable over its rivals in terms of the modeling capability.