An Estimation of Survival and Hazard Rate Functions of Exponential Rayleigh Distribution

In this paper, we used the maximum likelihood estimation method to find the estimation values ​​for survival and hazard rate functions of the Exponential Rayleigh distribution based on a sample of the real data for lung cancer and stomach cancer obtained from the Iraqi Ministry of Health and Environment, Department of Medical City, Tumor Teaching Hospital, depending on patients' diagnosis records and number of days the patient remains in the hospital until his death.

The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration.

Psychometric properties of the Burnout Inventory for Referees (BIR) for Brazilian Basketball Referees

El objetivo principal de este trabajo fue verificar las propiedades psicométricas del Inventario de Burnout para Árbitros en árbitros de baloncesto brasileños. Fueron evaluados un total de 395 árbitros de baloncesto (edad: 35.11 ± 9.18 años), de ambos sexos (masculino = 319 y femenino = 76), con un tiempo de experiencia promedio de 12.34 ± 7.83 años, quienes respondieron cuestionarios de identificación demográfica, Burnout Inventory for Brazilian Basketball Referees (BIR-AB) y Brunel Mood Scale for Basketball Referees (BRUMS-AB). La validez factorial se estimó mediante el análisis factorial confirmatorio (AFC) con el método de estimación de máxima verosimilitud. Como se rechazó la homocedasticidad, la comparación entre grupos se realizó mediante ANOVA con corrección de Welch seguido del post-test de Games-Howell. La correlación entre las puntuaciones de los factores BIR-AB y las variables edad y duración de la experiencia se evaluó mediante el análisis de correlación de Pearson (r). El nivel de significancia adoptado fue del 5%. Tras la realización del AFC e inserción del modelo jerárquico de segundo orden (MHSO), se propuso un nuevo modelo, denominado BIR-AB (Burnout Inventory for Referees para árbitros brasileños de baloncesto), que contiene dos dimensiones negativas (agotamiento físico y emocional y despersonalización) y una positiva (rendimiento deportivo), con índices de ajuste adecuados, se constató una confiabilidad aceptable e invariante entre el género y en la muestra de prueba / validación y la validez divergente. The main goal of this paper was to verify the psychometric properties of the Burnout Inventory for Referees on Brazilian basketball referees (BIR-AB). A total of 395 basketball referees were evaluated (age: 35.11 ± 9.18 years), of both gender (male = 319 and female = 76), with an average experience time of 12.34 ± 7.83 years, who answered demographic identification questionnaires, Burnout Inventory for Brazilian Basketball Referees (BIR-AB) and Brunel Mood Scale for Basketball Referees (BRUMS-AB). Factor validity was estimated using Confirmatory Factor Analysis (CFA) with the Maximum Likelihood estimation method. As homoscedasticity was rejected, the comparison between groups was performed using ANOVA with Welch's correction followed by the Games-Howell post-test. The correlation between the scores of the BIR-AB factors and the variables age and length of experience was assessed using Pearson's Correlation Analysis (r). The level of significance adopted was 5%. After the performance of the CFA and insertion of the second-order hierarchical model (MHSO), a new model was proposed, called BIR-AB, containing two negative dimensions (physical and emotional exhaustion and depersonalization) and a positive (sport performance), with adequate adjustment indexes, acceptable and invariant reliability between the gender and in the test/validation sample and the divergent validity was attested. O objetivo principal desse estudo foi verificar as propriedades psicométricas do Burnout Inventory for Referees para árbitros brasileiros de basquetebol. Foram avaliados 395 árbitros de basquetebol (idade: 35,11 ± 9,18 anos), de ambos os sexos (masculino=319 e feminino=76), com tempo médio de experiência de 12,34 ± 7,83 anos, que responderam aos questionários de identificação demográfica, Burnout Inventory for Brazilian Basketball Referees (BIR-AB) e Brunel Mood Scale for Basketball Referees (BRUMS-AB). A validade fatorial foi estimada utilizando-se a Análise Fatorial Confirmatória (AFC) com método de estimação da Máxima Verossimilhança. Como a homocedasticidade foi rejeitada, a comparação entre os grupos foi realizada por meio da ANOVA com correção de Welch seguido pelo pós-teste de Games-Howell. A correlação entre os escores dos fatores do BIR-AB e as variáveis idade e tempo de atuação foi avaliada a partir da Análise de Correlação de Pearson (r). O nível de significância adotado foi 5%. Após a realização da AFC e inserção do modelo hierárquico de segunda ordem (MHSO), um novo modelo foi proposto, chamado de BIR-AB (Burnout Inventory for Referees para árbitros brasileiros de basquetebol), contendo duas dimensões negativas (exaustão física e emocional e ) e uma positiva (desempenho esportivo), com índices adequados de ajustamento, confiabilidade aceitável e invariante entre os sexos e na amostra teste/validação e a validade divergente foi atestada.

The application of the Pareto distribution to approximate income distributions of wealthy households in Poland

The aim of the paper is to approximate the equivalent income distributions of wealthy households in particular socio-economic groups using the Pareto distribution, with parameters estimated by means of the maximum likelihood estimation method. Households whose income exceeded the established wealth threshold were classified as wealthy households. Income distributions of wealthy households are usually non-modal and heavy-tailed, thus, the Pareto distribution was applied as their theoretical model. The equivalent income of wealthy households in Poland was analysed in total and in particular socio-economic groups. The research was based on data from the 2014–2017 Household Budget Survey. Selected similarity measures were used to examine the degree to which the theoretical distributions proved consistent with the empirical ones. The obtained results confirmed the high level of consistency of empirical income distributions with the Pareto model. Moreover, very good approximations were obtained especially for wealthy households of employees and self-employed, as well as pensioners. Slightly worse results were obtained for the farmers group. Theoretical distributions well fitted to empirical data were used to estimate selected distribution characteristics, including measures of location, dispersion and inequality, and to compare the different groups in terms of their wealth.

Functional SAC model: With application to spatial econometrics

Spatial autoregressive combined (SAC) models have been widely studied in the literature for the analysis of spatial data in various areas such as geography, economics, demography, regional sciences. This is a linear model with scalar response and scalar explanatory variables which allows for spatial interactions in the dependent variables and the disturbances. In this work we extend this modeling approach from scalar to functional covariate. The parameters of the model are estimated via the maximum likelihood estimation method. A simulation study is conducted to evaluate the performance of the proposed methodology. As an illustration, the model is used to establish the relationship between unemployment and illiteracy in Senegal.

A multi-group higher-order factor analysis for studying the gender-effect in Teacher Job Satisfaction

Teachers’ performances also depend on whether and how they are satisfied with their job. Therefore, Teacher Job Satisfaction must be considered as the driver of teachers’ accomplishments. To plan future policies and improve the overall teaching process, it is crucial to understand which factors mostly contribute to Teacher Job Satisfaction. A Common Assessment Framework and Education questionnaire was administered to 163 Italian public secondary school teachers to collect data, and a second-order factor analysis was used to detect which factors impact on Teacher Job Satisfaction, and to what extent. This model-based approach guarantees to detect factors which respect important properties: unidimensionality and reliability. All the coefficients are estimated according to the maximum likelihood estimation method in order to make inference on the parameters and on the validity of the model. Moreover, a new multi-group test for higher-order factor analysis was proposed and implemented. Finally, we analyzed in detail whether the factors impacting Teacher Job Satisfaction are characterized by gender.

The Zubair-dagum Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.