Statistics

In this article, the estimation of parameters based on progressively type-II censored sample with random removals from the Weibull distribution is studied. The number of units removed at each failure time is assumed to follow a Beta-binomial distribution. Based on this type of censored sample, the maximum likelihood (ML) and approximate maximum likelihood (AML) estimators for the parameters of the Weibull distribution are derived. A Monte Carlo simulation study is also conducted to compare the performance of ML and AML estimators under progressively type-II censoring with the different random schemes.

Bu araştırmada ‘veri, sayma ve olasılık’ konusun teknoloji destekli öğretiminin ortaöğretim düzeyindeki 10. Sınıf öğrencileri üzerindeki etkisi incelenmiştir. Okul ders kitaplarının ve yürütülen FATİH Projesi kapsamındaki ders materyallerinin, öğretim  programının kazanım ve vurgularına ne derece uyduğu ortaya konmaya çalışılmıştır.
Araştırma kapsamında yanıt aranan sorular;
1. 10. Sınıf öğrencileri, 9. Sınıf öğretim programının son konularından olan ‘veri, sayma ve olasılık’ öğrenme alanının ‘veri’ ünitesi için kalıcı bir öğrenme geliştirebilmişler midir?
2. ‘Veri, sayma ve olasılık’ öğrenme alanının ‘veri’ ünitesinin teknoloji destekli öğretim yaklaşımları ve klasik öğretim metotları ile öğretmen tarafından öğretilmesi ve öğrenci tarafından öğrenilmesi süreçlerinde göze çarpan faktörler nelerdir?
3. Öğretmen ve öğrenciler istatistik okuryazarı olarak kendilerini ne düzeyde görmektedir?
4. Matematik didaktiği genelinde ve didaktiksel durum teorisi çerçevesinde ‘veri’ ünitesinin öğretilmesi ve öğrenilmesi süreçleri ne gibi didaktik antlaşmaları içermektedir?
5. Tasarlanmış ders programlarının uygulaması sonunda klasik öğretim yöntemleri  ile teknoloji destekli öğretim yöntemlerinin birbirlerine üstünlükleri öğretmen ve öğrenci  perspektifinden nelerdir?
6. 9. Sınıf matematik ders kitabının veri ünitesi antropolojik didaktik yaklaşımı  çerçevesinde, öğretim programı hedef kazanımlarına ve öğretim süreçlerinde dikkate  alınmasının istenildiği tavsiyelere ne derece uymaktadır?
Öğretim süreci klasik öğretim metotları ve teknoloji destekli öğretim metotları dikkate alınarak iki farklı şekilde tasarlanmıştır. Bu süreçler Eskişehir ili Tepebaşı ilçesi ortaöğretim kurumlarında uygulanmıştır. Araştırma deseni olarak nitel araştırma desenlerinden durum çalışması yürütülmüştür. Genelleyici bir yargıya ulaşma çabası gözetilmemiştir. Araştırmada kullanılan örnekleme yöntemi, bu okullar arasından olmak
üzere olasılıklı olmayan yöntemlerden, yargısal örneklemedir. Araştırmada, öğretim programlarında yeni yerini alan istatistik konuları ile öğretimde teknoloji kullanımı ortak bir perspektiften incelenmiştir. Araştırma bu açıdan önemli olup benzer araştırma ve projelere kaynaklık edebilecektir. Araştırma neticesinde öğrencilerin veri ünitesinin kavramlarını karıştırdıkları ortaya konmuştur. Öğrencilerin gerek klasik gerekse teknoloji destekli öğretimlere tam anlamıyla katılamadığı gözlemlenmiş, daha çok öğretmen merkezli bir öğretimin farklı iki öğretim yaklaşımında da ağır bastığı görülmüştür. Öğrencilerde konuya dair rastlanan kavram yanılgıları ve problemler paylaşılmıştır. Teknolojinin bu ünite kapsamında kullanılmasının şart olduğu birçok
öğretmen tarafından vurgulanmış olsa da bu vurgulara rağmen öğretmenlerin tam verimle
ders içine teknolojiyi entegre edemedikleri ortaya konmuştur. Öğrenciler ise konu kapsamında teknoloji kullanımının sürat kazandırdığını vurgulamıştır. Ancak öğrenciler tarafından programın arka planda yaptığı işlemlerin merak konusu olmadığı dikkat çekmektedir. Öğrenciler onlara dağıtılacak tabletlerle derse daha çok ortak olabileceklerini ifade etmişlerdir. Öğretmenlerin ifadeleri de bunu destekler niteliktedir.
Öğretmenler FATİH projesi kapsamında şu halde yürütülen sistemde etkileşimli tahtanın bir tür ekran görüntüsü yansıtıcısı gibi kullanıldığını ifade etmişlerdir. E-içerik eksikliği öğretmenlerce vurgulanmıştır. Ayrıca öğretmenlerin ders içeriği sıkıntıları ve akıllı tahtalara bilgi akışının sağlanmasındaki teknik arızalar önemli vurgulardır. Ders kitaplarının teknoloji uygulamalarına ve gerçek hayat problemlerine yeteri kadar yer
vermediği söylenebilir. İstatistik okuryazarlığı konusunda öğrencilerin tam bir yeterlilik durumundan bahsedilemeyip, bunun yanında teknoloji okuryazarlığının da hem öğrenci hem de öğretmen için ciddi bir engel olduğu ortaya konmuştur. Hizmet öncesi ve hizmetçi eğitim eksikliği yine öğretmenlerce dikkat çekilen bir noktadır.
Anahtar Kelimeler: İstatistik Öğretimi, Didaktiksel Durum Teorisi, Didaktiksel Dönüşüm Teorisi, VUstat, İstatistik Okuryazarlığı, Teknolojik Pedagojik Alan Bilgisi, Teknoloji Destekli Matematik Öğretimi

The knowledge of the probability density function of wind speed is key information for the determination of wind energy potential of the specified region. In the literature, the Weibull distribution is a widely-used and accepted distribution to express the probability density function of wind speed data. However, the Weibull distribution does not exhibit a good fitting for all wind speed data measured at different geographical locations throughout the world. Thus, in this study, it is proposed that a better fitting of wind speed data and a better estimating wind power density are possible with the new modified Weibull distribution (MWD). We also compare the performance of the MWD relative to the Weibull distribution by using wind speed data measured in different regions of Turkey. The results state that the MWD shows good fitting for the most of the considered wind speed data cases. Thus, the MWD can be an alternative tool for the assessment of wind energy potential.

The wind energy potential of a specified region can be estimated using the distribution of wind speed. Thus, 11 finding appropriate wind speed distribution is essential. Weibull distribution (WD) is the most popular 12 distribution in wind energy literature. Besides WD, various statistical distributions have been widely-used as 13 reference distributions to characterize wind speed. However, it is observed that these distributions may not

This study introduces a new estimation approach that could be used in calculating the Weibull parameters for the estimation of wind power. This new approach, called the method of multi-objective moments (MUOM), proposes minimization of the squared deviances between the first three population moments and corresponding sample moments. In the proposed MUOM, the third moment, which is used in the formula of wind power, is a key function since it provides a significant contribution to the correct prediction of wind energy. In order to demonstrate the performance of the proposed MUOM, it is compared with the well-known estimation methods such as the maximum likelihood, modified maximum likelihood, moment and energy pattern factor. In comparative analysis, the performance of the considered methods is evaluated on the actual wind speed data measured different time periods according to various goodness of fit criteria. The obtained results indicate that the MUOM definitely provides more accurate estimates than other well-known methods in estimating wind power based on the Weibull distribution. Thus, the MUOM can be used as an improved method in estimating wind power.

In this study, the internodes locations of the roots formed in cuttings were investigated. In addition, it has been investigated whether there is a difference in root formation density for grapevine types. SO4, 5BB, Lot and 8B grapevine rootstocks obtained from Tekirdağ Viticulture and Research Institute were used and the experiment was conducted in the same institute. The cuttings were planted in deep sand boxes prepared with 15 cm row spacing (RS) and intra-row spacing (IS) on March 3, 2017. After defoliation, cuttings were removed from the boxes and measured on November 15, 2017. Root measurements were made from the left, right, opposite and just below the internodes. The criteria used were the number of roots, root length, root weight and root thickness. The two-factor factorial design model was used instead of the single-factor design model, which frequently appeared in the literature. Thus, the differences between the internodes and the differences between the grapevine types could be considered as the main factors examined. In addition, the use of two-factor experimental design allowed to investigate the interaction of grapevine types and internodes. All findings were presented and interpreted. As a result there were statistical differences between the internodes and rootstocks in terms of number of roots, root length, root weight and root thickness.

The knowledge of the probability density function of wind speed is key information for determining wind energy potential of the specified region. In literature, the Weibull distribution is widely-used and accepted distribution to express the probability density function of wind speed data. However, the Weibull distribution does not exhibit good fitting for all wind speed data measured at different geographical locations throughout the world. Thus, in this study, it is proposed that a better fitting of wind speed data and a better estimating wind power density is possible with new modified Weibull distribution (MWD). Also, we compare the performance of the MWD relative to the Weibull distribution by using wind speed data measured in the different regions of Turkey. The results point out that the MWD shows good fitting for most of the considered wind speed data cases. Thus, the MWD can be alternative for assessment of wind energy potential.

Since the Weibull distribution has been accepted reference distribution in wind energy field, topics on its parameter estimation methods have been attracted issue. In this context, the literature have generally focused on non-robust methods which may yield questionable results in the cases of unusual and contaminated wind speed data. This paper discusses some robust estimation methods of the Weibull distribution for unusual wind speed data cases. The considered robust methods are evaluated by using artificially generated unusual wind speed data cases. It was found that some of the considered robust methods provide reliable results compared classical ones. Also, the same results are observed for the estimation of mean power density error. As a result, analyzes performed shows that robust and efficient classical methods can be used together to check results.

In the case of censored data, it is often seen that the error distribution is skewed and multimodal. Ordinary least squares (OLS) estimator, which often gives biased and inconsistent results for censored data, and Tobit estimator, which is frequently used in censored data estimation and gives inconsistent results when some assumptions are not met, are also problematic in the presence of skewed and multimodal distribution of error terms. A new estimator is proposed as an alternative to the two conventional estimators used in the case of censored data. For censored regression model, an estimation method, known as partial adaptive or quasi-maximum likelihood estimator, has been introduced based on the alpha skewed logistic distribution, which is a flexible error distribution. According to the bias and mean square error (MSE), new estimator is superior for estimating the coefficients of the censored regression model under the skewed and multimodal error distribution.

vii students couldn't participate properly in lessons in both teaching approaches and there was mostly teacher-centered teaching. The common misconceptions and problems of students on the subject were shared. Using of technology in this unit was highlighted by many teachers. On the other hand, teachers can not integrate technology into the class with high yield. Students often emphasized that using of technology provided more speed on process steps. It demonstrated that students did not care about operations performed in the background of the program. Students stated that they would be active in lessons with tablets that would be distributed to them. These statements are supported by teachers. Teachers stated that interactive board that distributed in the scope of the FATİH Project is only used as a screen reflector or display. The lack of e-content is highlighted by teachers. Also, teacher's course content problems and technical breakdown in the flow of data to the smart boards are important points. It can be said that textbooks do not contain enough technology applications and real-life problems. Statistical literacy of students is not adequate. Moreover, technology literacy is a barrier in the teaching process for both teachers and students. The lack of pre-service and in-service training are mentioned by teachers.

This study investigates the spatio-temporal structure of the pandemic in Türkiye during the normalization process. An analysis has been conducted based on spatial and space-time scan statistics of the province-based numbers of confirmed COVID-19 cases during the normalization process from February 27 to May 7, 2021. The clusters affected by regional application differences has determined. The increase in cases has been observed, and the risk classes that supported the spatial relationship have been determined. Positive spatial relationships have been observed. Moran I measurements have also directly overlapped with the developments in the timeline of the COVID-19 pandemic in Türkiye. Local Moran I analysis has shown the transition of clusters from different regions to others over time. According to the results, controlled normalization has not happened as expected and the increase in the number of cases eventually led to the start of a total lockdown. Spatial and spatiotemporal analysis may show how to respond to a potential new pandemic. Regulations that vary from region to region can be meaningless depending on the spatial interaction. Decision makers may benefit in the future from these analyses, which reveal the results of experience to control current worsening scenarios.

Introduction: Pandemic caused by SARS-CoV-2 infection has been an important health problem worldwide for the last 3 years. The pathogenesis and consequences of liver injury developed in COVID-19 disease are still unclear. We investigated the prevalence of liver function tests (LFTs) abnormalities in COVID-19 patients, their relationship with drugs, the difference between severe and non-severe COVID-19 patients, and the results of the course of LFTs among patients hospitalized in intensive care units and clinics. Methods: 389 patients who applied to Eskişehir City Hospital between March 2020 and October 2020 were included in the study. Demographic data of RT-PCR (+) patients and RT-PCR (-) control groups (age, gender, comorbidities, symptoms), laboratory parameters, radiological examinations, follow-ups in the clinics and intensive care units, drugs used for the infection were collected retrospectively. All patients with COVID-19 were classified as severe cases or mild to moderate cases groups. Results: Abnormal LFTs were found in 115 (35.2%) of 321 patients with RT-PCR(+), and in 10 (14.7%) of 68 patients in the PCR(-) control group. LFTs at the time of hospitalization were 10.3%, 22.7%, 4.9%, 11.4% and 1.2% in the patient group, respectively; in the control group, it was 1.9%, 2.9%, 2%, 3.3%, 0.8% (p=0.610, p=0.00, p=0.269, p=0.198, p=0.158). There was a significant increase in LFTs in patients who received antibiotics (Levofloxacin, Ceftriaxone, Clarithromycin, Tazobactam, Carbapenem), low molecular weight heparins and antiviral (favipravir) treatments (p=0.001, p=0.001, p=0.001). While the increase in LFTs were significant in the mild (40.2%; 8.2%) and severe groups (41.2%; 5.2%), the number of patients with elevated LFTs in the control group was low (0.5%). Conclusion: Liver damage is common in SARS-CoV-2 infection, but it is quite mild. Patients with severe COVID-19 have a higher frequency of abnormal LFTs than those with mild disease. Disease severity, pre-existing liver disease, and advanced age are risk factors for liver damage. Druginduced liver injury, systemic inflammatory response syndrome, and hypoxia-induced liver injury may be the main etiological factors for liver injury in COVID-19.

AIM: The aim of the study was to evaluate the clinical features and risk factors affecting bleeding in patients with angiodysplasia. MATERIA L AND METHOD: This retrospective study was conducted between January 2016 and December 2019, and included patients who underwent endoscopy/colonoscopy examination for any reason at two institutions (n=2177). Patients with angiodysplasia were divided into two groups according to their bleeding status, and their clinical features and risk factors affecting bleeding were analyzed. RESULTS: Angiodysplasia was detected in 44 (2.02%) patients who underwent endoscopy and colonoscopy. Bleeding was detected in 25% (n=11) of patients with angiodysplasia. Warfarin use frequency (p=0.016) and heart disease frequency (p=0.008) were higher in patients with angiodysplasia with bleeding. Hemoglobin (p=0.001), hematocrit (p < 0.001), platelet levels (p=0.009) and total iron binding capacity (p=0.036) were found to be significantly lower in patients with blee...

In a dynamic system such as flight control systems, faults caused by sensors, actuators and controllers can bring on unwanted reactions, reduce overall system efficiency and performance or even lead to failure of the overall, therefore it is required to detect such faults as soon as possible to isolate them accurately. During the past three decades a variety of methods have been developed to detect faults in processes and control systems. In this study, a longitudinal model of a fighter aircraft was selected as an example of a flight control system. Using data-driven methods based on multivariate statistical techniques, such as principal component analysis we tried to detect faults in the sensors. In these methods, calculations will be done based on the calculation of Hotelling's T^2 statistic and squared prediction error (SPE) statistic of the observation vector, and comparing with the statistics of the respective areas, as well as threshold levels, normal or abnormal status were detected. Keywords-flight control system, sensor fault, fault detection, longitudinal aircraft dynamic, data-driven method, multivariate statistical method, principle component analysis.

In a dynamic system such as flight control systems, faults caused by sensors, actuators and controllers can bring on unwanted reactions, reduce overall system efficiency and performance or even lead to failure of the overall, therefore it is required to detect such faults as soon as possible to isolate them accurately. During the past three decades a variety of methods have been developed to detect faults in processes and control systems. In this study, a longitudinal model of a fighter aircraft was selected as an example of a flight control system. Using data-driven methods based on multivariate statistical techniques, such as principal component analysis we tried to detect faults in the sensors. In these methods, calculations will be done based on the calculation of Hotelling's T 2 statistic and squared prediction error (SPE) statistic of the observation vector, and comparing with the statistics of the respective areas, as well as threshold levels, normal or abnormal status were detected.

In a dynamic system such as flight control systems, faults caused by sensors, actuators and controllers can bring on unwanted reactions, reduce overall system efficiency and performance or even lead to failure of the overall, therefore it is required to detect such faults as soon as possible to isolate them accurately. During the past three decades a variety of methods have been developed to detect faults in processes and control systems. In this study, a longitudinal model of a fighter aircraft was selected as an example of a flight control system. Using data-driven methods based on multivariate statistical techniques, such as principal component analysis we tried to detect faults in the sensors. In these methods, calculations will be done based on the calculation of Hotelling's T 2 statistic and squared prediction error (SPE) statistic of the observation vector, and comparing with the statistics of the respective areas, as well as threshold levels, normal or abnormal status were detected.

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n = 2, 3, 4 by using MATLAB.

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n = 2, 3, 4 by using MATLAB.