Design of General Entropy-Constrained Successively Refinable Unrestricted Polar Quantizer

The medical data are often filed for each patient in clinical studies in order to inform decision-making. Usually, medical data are generally skewed to the right, and skewed distributions can be the appropriate candidates in making inferences using Bayesian framework. Furthermore, the Bayesian estimators of skewed distribution can be used to tackle the problem of decision-making in medicine and health management under uncertainty. For medical diagnosis, physician can use the Bayesian estimators to quantify the effects of the evidence in increasing the probability that the patient has the particular disease considering the prior information. The present study focuses the development of Bayesian estimators for three-parameter Frechet distribution using noninformative prior and gamma prior under LINEX (linear exponential) and general entropy (GE) loss functions. Since the Bayesian estimators cannot be expressed in closed forms, approximate Bayesian estimates are discussed via Lindley’s approximation. These results are compared with their maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under general entropy loss function with noninformative prior (BGENP) provide the smallest mean square error for all sample sizes and different values of parameters. Furthermore, a data set about the survival times of a group of patients suffering from head and neck cancer is analyzed for illustration purposes.

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GENERAL ENTROPY OF GENERAL MEASURES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488502001442 ◽

2002 ◽

Vol 10 (03) ◽

pp. 213-225 ◽

Cited By ~ 16

Author(s):

ALEXANDER DUKHOVNY

Keyword(s):

Sufficient Condition ◽

Independence Property ◽

General Entropy ◽

Definition Of ◽

Additive Measures ◽

Countable Case

The concept of entropy is an important part of the theory of additive measures. In this paper, a definition of entropy is introduced for general (not necessarily additive) measures as the infinum of the Shannon entropies of "subordinate" additive measures. Several properties of the general entropy are discussed and proved. Some of the properties require that the measure belongs to the class of so-called "equientropic" general measures introduced and studied in this paper. The definition of general entropy is extended to the countable case for which a sufficient condition of convergence is proved. We introduce a method of "conditional combination" of general measures and prove that in that case the general entropy possesses the "subset independence" property.

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General entropy model of line segments uncertainty in GIS

Geo-spatial Information Science ◽

10.1007/s11806-006-0149-7 ◽

2007 ◽

Vol 10 (1) ◽

pp. 61-66 ◽

Cited By ~ 1

Author(s):

Yufeng Shi ◽

Wenzhong Shi

Keyword(s):

Entropy Model ◽

Line Segments ◽

General Entropy

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A New Approach to Thermodynamics of Simple Mixtures

Zeitschrift für Naturforschung A ◽

10.1515/zna-1973-1107 ◽

1973 ◽

Vol 28 (11) ◽

pp. 1801-1813 ◽

Cited By ~ 30

Author(s):

Ingo Müller

Keyword(s):

Thermal Diffusion ◽

Constitutive Relations ◽

Absolute Temperature ◽

New Approach ◽

Chemical Potentials ◽

General Entropy ◽

Entropy Principle ◽

The Absolute

A general entropy principle is utilized to derive restrictions on the constitutive relations for simple mixtures. The absolute temperature and chemical potentials are introduced in a novel manner and the equality of the coefficients of thermal diffusion and of the diffusion-thermo coefficients is proved for a subclass of simple mixtures by use of macroscopic arguments.

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General entropy criteria for inverse problems, with applications to data compression, pattern classification, and cluster analysis

IEEE Transactions on Information Theory ◽

10.1109/18.50370 ◽

1990 ◽

Vol 36 (1) ◽

pp. 23-30 ◽

Cited By ~ 57

Author(s):

L.K. Jones ◽

C.L. Byrne

Keyword(s):

Cluster Analysis ◽

Inverse Problems ◽

Data Compression ◽

Pattern Classification ◽

General Entropy ◽

And Cluster Analysis

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PENDEKATAN BAYESIAN GELF UNTUK ESTIMASI PARAMETER MODEL SURVIVAL RAYLEIGH DENGAN PRIOR UNIFORM

Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya ◽

10.26418/bbimst.v8i3.33867 ◽

2019 ◽

Vol 8 (3) ◽

Author(s):

Petty Jelda, Setyo Wira Rizki, Nurfitri Imro’ah

Keyword(s):

Loss Function ◽

Entropy Loss ◽

General Entropy ◽

General Entropy Loss Function ◽

Primary Billiary Cirrhosis

Data survival adalah data yang menunjukkan waktu suatu individu atau objek yang dapat bertahan hidup hingga terjadinya suatu kegagalan atau kejadian tertentu. Tujuan dari penelitian ini adalah untuk menentukan model survival dan model hazard estimasi parameter berdistribusi Rayleigh dengan metode Bayesian General Entropy Loss Function (GELF) menggunakan prior Uniform. Estimasi parameter fungsi survival dan fungsi hazard Bayesian GELF didapat dengan mencari nilai estimasi parameter Bayesian GELF. Selanjutnya diterapkan pada data 175 pasien penderita Primary Billiary Cirrhosis (PBC) yang diperoleh dari program R versi 3.3.0 untuk mengetahui peluang individu dapat bertahan hidup. Nilai estimasi parameter Bayesian GELF dari data yang dihitung menggunakan progam R adalah 896,8008. Berdasarkan hasil estimasi parameter model survival distribusi Rayleigh metode Bayesian GELF dapat diketahui peluang seorang penderita penyakit PBC untuk bertahan hidup semakin lama semakin kecil (mendekati nol), dengan resiko kematian yang semakin besar.Kata Kunci : Distribusi Rayleigh, Bayesian GELF, Prior Uniform.

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