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Related Concept Videos

Hazard Rate01:11

Hazard Rate

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The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
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Hazard Ratio01:12

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The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
For example, in a clinical trial...
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
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Odds Ratio01:09

Odds Ratio

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The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
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Applications of Normal Distribution01:22

Applications of Normal Distribution

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The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal distribution of heights of persons, such that many can pass through it easily without striking their heads. The normal distribution can also determine the probability of a person having a height less than a specific height.
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Hazard rate estimation when the measurement error has a normal or logistic distribution.

Parviz Nasiri1, Rougheih Kheirazar1, Abbas Rasouli2

  • 1Department of Statistics, University of Payam Noor, 19395-4697, Tehran, Iran.

Heliyon
|March 25, 2024
PubMed
Summary

Measurement errors in statistical data reduce accuracy. This study estimates the hazard rate function, crucial for reliability, even with measurement errors from normal or logistic distributions, using advanced polynomial estimation methods.

Keywords:
BandwidthKernel density estimationLifetime dataLogistic distributionMean squared error

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Data Analysis

Background:

  • Measurement error is prevalent in scientific data, impacting statistical analysis accuracy.
  • Ignoring measurement errors leads to poor goodness-of-fit for distribution parameter estimators.
  • The hazard rate function is a critical metric in reliability analysis.

Purpose of the Study:

  • To investigate the hazard rate function in the presence of measurement error.
  • To address the accuracy limitations caused by ignoring measurement errors in statistical modeling.
  • To develop methods for estimating the hazard rate function under data contamination.

Main Methods:

  • Utilized local time polynomial estimator methods for density function estimation.
  • Estimated the hazard rate function considering measurement errors from normal or logistic distributions.
  • Analyzed the impact of contamination degrees (15% and 30%) on the estimation.

Main Results:

  • Developed an accurate method for estimating the hazard rate function despite measurement errors.
  • Demonstrated the effectiveness of local time polynomial estimators in handling contaminated data.
  • Numerical analysis confirmed the performance of the proposed estimation techniques.

Conclusions:

  • Accurate hazard rate estimation is achievable even with measurement error in statistical data.
  • The proposed methods provide reliable estimators for reliability criteria under data contamination.
  • This research offers improved statistical tools for scientific data analysis in various fields.