Medyan Sıralı Küme Örneklemesine Dayalı Ters Nadarajah-Haghighi Dağılımının Parametre Tahmini

Abstract

Ters Nadarajah–Haghighi dağılımı, monoton olmayan tehlike oranı yapısına sahip yaşam süresi verilerinin modellenmesindeki esnekliği nedeniyle son yıllarda dikkat çekmektedir. Bu çalışmada, söz konusu dağılım için parametre tahmini iki rekabetçi örnekleme tasarımı altında incelenmektedir: basit rastgele örnekleme ve medyan sıralı kümeleme örneklemesi. Model parametrelerine ait maksimum olabilirlik tahmin edicileri her iki örnekleme şeması için türetilmiştir. Önerilen tahmin edicilerin etkinliğini değerlendirmek amacıyla, farklı örneklem büyüklükleri ve parametre yapılandırmaları altında yanlılık ve ortalama kare hata ölçütlerine dayalı kapsamlı bir Monte Carlo simülasyon çalışması gerçekleştirilmiştir. Simülasyon sonuçları, medyan sıralı kümeleme örneklemesinin basit rastgele örneklemeye kıyasla daha hassas ve daha etkin parametre tahminleri sağladığını tutarlı biçimde ortaya koymaktadır. Elde edilen bulgular, örnekleme sürecine sıralama bilgisinin dâhil edilmesinin sağladığı avantajı vurgulamakta ve önerilen yaklaşımın ters Nadarajah–Haghighi dağılımı için daha etkili bir çıkarım çerçevesi sunduğunu göstermektedir. Bu çalışma, söz konusu dağılım altında parametre tahmini için örnekleme tasarımlarının kapsamlı bir karşılaştırmasını sunması ve medyan sıralı kümeleme örneklemesiyle elde edilen pratik kazanımları ortaya koyması bakımından literatüre katkı sağlamaktadır.

Keywords

• Medyan sıralı kümeleme örneklemesi
• basit rastgele örnekleme
• en çok olabilirlik tahmin edicisi
• ters Nadarajah-Haghighi dağılımı

Parameter Estimation for the Inverted Nadarajah-Haghighi Distribution Based on Median Ranked Set Sampling

Abstract

The inverted Nadarajah–Haghighi distribution has recently attracted attention due to its flexibility in modeling lifetime data with non-monotonic hazard rate structures. In this study, parameter estimation for this distribution is investigated under two competing sampling designs, namely simple random sampling and median ranked set sampling. Maximum likelihood estimators of the model parameters are derived for both sampling schemes. To evaluate the efficiency of the proposed estimators, an extensive Monte Carlo simulation study is conducted based on bias and mean squared error criteria over different sample sizes and parameter configurations. The simulation results consistently demonstrate that median ranked set sampling provides more precise and efficient parameter estimates compared to simple random sampling. The findings highlight the advantage of incorporating ranking information into the sampling process and show that the proposed approach offers a more effective inference framework for the inverted Nadarajah–Haghighi distribution. This study contributes to the existing literature by presenting a comprehensive comparison of sampling designs for parameter estimation within this distributional setting and by demonstrating the practical gains achieved through median ranked set sampling.

Keywords

• Median ranked set sampling
• simple random sampling
• maximum likelihood estimator
• inverted Nadarajah-Haghighi distribution

Supporting Institution

The authors received no financial support for this study.

Ethical Statement

This study does not require ethics committee approval because no human or animal data were used.

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