scholarly journals Estimating of Survival Function under Type One Censoring Sample for Mixture Distribution

2020 ◽  
Vol 33 (4) ◽  
pp. 102
Author(s):  
Qesma S. Abadi ◽  
Iden H. AL-Kanani
Keyword(s):  
Probability Density Function ◽  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Likelihood Estimator ◽  
Censored Sample ◽  
Newton Raphson

In this article, it is interesting to estimate and derive the three parameters which contain two scales parameters and one shape parameter of a new mixture distribution for the singly type one censored data which is the branch of right censored sample. Then to define some special mathematical and statistical properties for this new mixture distribution which is considered one of the continuous distributions characterized by its flexibility. Next,  using maximum likelihood estimator method for singly type one censored data based on the Newton-Raphson matrix procedure to find and estimate values of these three parameter by utilizing the real data taken from the National Center for Research and Treatment of Hematology/University of Mustansiriyah for leukemia diseases. After that we find and derive the estimate of probability density function, estimate survival function and finally estimate the hazard function. 

scholarly journals Non Bayesian estimation for survival and hazard function of weighted Rayleigh distribution (b)

2020 ◽  
pp. 3059-3071
Author(s):  
Saad Adnan Zain
Keyword(s):  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
New Class ◽  
The Moment ◽  
Two Parameters

In this paper, we proposed a new class of Weighted Rayleigh Distribution based on two parameters, one is scale parameter and the other is shape parameter which introduced in Rayleigh distribution. The main properties of this class are derived and investigated in . The moment method and maximum likelihood method are used to obtain estimators of parameters, survival function and hazard function. Real data sets are collected to investigate two methods which depend it in this study. A comparison was made between two methods of estimation.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

Erlang mixture distribution with application on COVID-19 cases in egypt

2021 ◽  
pp. 2150015
Author(s):  
M. M. E. Abd El-Monsef
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Finite Mixture ◽  
Erlang Distribution ◽  
Parameter Estimates ◽  
Proposed Model ◽  
Shape Characteristics ◽  
Erlang Distributions ◽  
Special Case

In this paper, a finite mixture of m-Erlang distributions is proposed. Different moments, shape characteristics and parameter estimates of the proposed model are also provided. The proposed mixture has the property that it has a bounded hazard function. A special case of the mixed Erlang distribution is introduced and discussed. In addition, a predictive technique is introduced to estimate the needed number of mixture components to fit a certain data. A real data concerning the confirmed COVID-19 cases in Egypt is introduced to utilize the predictive estimation technique. Two more real datasets are used to examine the flexibility of the proposed model.

scholarly journals Estimasi Fungsi Survival dan Fungsi Hazard Kumulatif Pada Data Survival Pederita Multiple Myeloma Serta Faktor-faktor yang Mempengaruhi Waktu Survivalnya

Intersections ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 33-43
Author(s):  
Toto Hermawan ◽  
Dwi Nurrohmah ◽  
Ismi Fathul Jannah
Keyword(s):  
Multiple Myeloma ◽  
Distribution Function ◽  
Data Analysis ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Hazard Function ◽  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution

Multiple myeloma is an infectious disease characterized by the accumulation of abnormal plasma cells, a type of white blood cell, in the bone marrow. The main objective of this data analysis is to investigate the effect of Bun, Ca, Pcells and Protein risk factors on the survival time of multiple myeloma patients from diagnosis to death. In the survival data analysis, the observed random variable T is the time needed to achieve success. To explain a random variable, the cumulative distribution function or the probability density function can be used. In survival analysis, the function of the random variable that becomes important is the survival function and the hazard function which can be derived using the cumulative distribution function or the probability density function. In general, it is difficult to determine the survival function or hazard function of a population group with certainty. However, the survival function or hazard function can still be approximated by certain estimation methods. The Kaplan-Meier method can be used to find estimators of the survival function of a population. Meanwhile, to find the estimator of the cumuative hazard function, the Nelson-Aalen method can be used. From the variables studied, it turned out that the one that gave the most significant effect was the Bun variable, namely blood urea nitrogen levels using both the exponential and weibull distribution. However, by using the weibull distribution, the presence of Bence Jones Protein in urine also has a quite real effect

scholarly journals Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Ashok Shanubhogue ◽  
N. R. Jain
Keyword(s):  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Reliability Function ◽  
Minimum Variance ◽  
Unbiased Estimation ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

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