Sains Malaysiana 45(11)(2016): 1773–1777

On the Estimation of Three Parameters Lognormal Distribution Based on Fuzzy Life Time Data

(Anggaran Taburan Lognormal Tiga Parameter Berdasarkan Data Masa Hayat yang Kabur)

MUHAMMAD SHAFIQ¹*, ALAMGIR² & MUHAMMAD ATIF²

¹Department of Economics, Kohat University of Science and Technology, Kohat

²Department of Statistics, University of Peshawar, Pakistan

Received: 10 June 2015/Accepted: 14 June 2016

ABSTRACT

Countless statistical tools are available to extract information from data. Life time modeling is considered as one of the most prominent fields of statistics, which is evident from the developments made in this field in the last few decades. Almost every statistic for life time analysis is based on precise life time observations, however, life time is not a precise measurement but more or less fuzzy. Therefore, in addition to classical statistical tools, fuzzy number approaches to describe life time data are more suitable. In order to incorporate fuzziness of the observations, fuzzy estimators for the three parameter lognormal distribution were suggested. The proposed estimators cover stochastic variation as well as fuzziness of the observations.

Keywords: Characterizing function; fuzzy number; life time; non-precise data

ABSTRAK

Terdapat banyak perkakasan statistik tersedia untuk mengekstrak maklumat daripada data. Pemodelan masa hayat dianggap sebagai salah satu bidang statistik yang paling menonjol. Ini jelas daripada pembangunan bidang ini sejak beberapa dekad yang lalu. Hampir setiap statistik untuk analisis masa hayat adalah berasaskan pemerhatian masa hayat yang tepat, walau bagaimanapun, masa hayat bukanlah suatu pengukuran yang tepat tetapi lebih atau kurang kabur. Oleh itu, sebagai tambahan kepada perkakas statistik klasik, pendekatan nombor kabur untuk menggambarkan data masa hayat adalah lebih sesuai. Dalam usaha untuk menggabungkan kekaburan daripada pemerhatian, penganggaran kabur untuk taburan tiga parameter lognormal telah dicadangkan. Penganggaran yang dicadangkan meliputi kelainan stokastik serta kekaburan daripada pemerhatian.

Kata kunci: Data tidak tepat; fungsi pencirian; masa hayat; nombor kabur

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*Corresponding author; email: mshafiq_stat@yahoo.com