independently distributed

USAGE SUMMARY

The phrase "independently distributed" is correct and usable in written English.
It is typically used in statistics and probability theory to describe random variables that are not influenced by each other. Example: "In this experiment, we assume that the samples are independently distributed to ensure the validity of our results."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

Suppose that the lifetimes are independently distributed, and also independent from the censoring mechanism and censoring is random and noninformative.

Journal of Statistical Distributions and Applications

We assume independent fading with identically and independently distributed (i.i.d) mirror carrier channel coefficients.

EURASIP Journal on Wireless Communications and Networking

The band is still independently distributed by The Drop label, and as of 2009, have handled distribution themselves in Europe.

Wikipedia

It's homemade art independently distributed and inventively promoted.

The New York Times - Arts

Heaven Is for Real grossed $91m in the US for Sony, while the independently distributed God's Not Dead made $60m.

The Guardian - Film

Production costs are independently distributed and privately learned by the producer in each supply chain.

International Journal of Industrial Organization

It became the first independently distributed hip-hop album to debut at No 1 on the Billboard album charts, but received poor reviews.

The Guardian - Music

Before he had turned 20, his first album, Blue Slide Park (2011), became the first independently distributed debut to top the Billboard charts since 1995.

The Guardian - Music

It assumes that some of prognostic variables are continuous and others are categorical and that they are independently distributed.

Contemporary Clinical Trials

The key feature is not that the values are private but rather that they are independently distributed.

Auction Theory

Past research on environmental perceptions has, for the most part, treated responses as independently distributed across a given study area.

Landscape and Urban Planning

Expert writing Tips

Best practice

When using "independently distributed" in statistical contexts, clearly define the variables or elements to which the phrase applies to avoid ambiguity.

Common error

Avoid assuming that variables are "independently distributed" without proper statistical testing. False assumptions can lead to inaccurate models and erroneous conclusions.

Linguistic Context

The phrase "independently distributed" functions as an adverbial modifier describing how something is distributed. It specifies that the distribution of one item or variable does not affect the distribution of others. Ludwig confirms its correct usage in various contexts.

Expression frequency: Very common

Frequent in

Science

75%

News & Media

10%

Wiki

5%

Less common in

Formal & Business

3%

Reference

2%

Social Media

1%

Ludwig's WRAP-UP

In summary, "independently distributed" is a common phrase, particularly in scientific and statistical contexts, used to describe variables or events that do not influence each other. As Ludwig AI confirms, the phrase is grammatically correct and widely accepted. When using this phrase, it's important to ensure the assumption of independence is valid. Alternatives like "statistically independent" or "uncorrelated" can be used depending on the specific nuance. The phrase appears most frequently in science, news, and media sources. Remember to avoid assuming independence without verification, as this can lead to inaccurate conclusions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

statistically independent

This term is more specific to statistics, indicating a lack of statistical correlation.

mutually independent

Highlights the lack of influence each element has on the others within a group.

uncorrelated

Focuses on the absence of a linear relationship between variables.

not correlated

A simpler way to express the lack of correlation.

independently allocated

Specifies that the distribution process is done independently.

randomly assigned

Emphasizes the randomness and lack of systematic assignment.

separately distributed

Suggests a distribution process that treats each element in isolation.

individually distributed

Focuses on the individual nature of the distribution.

independently dispersed

Highlights the scattering or spreading of elements without mutual influence.

not dependent

A general way to indicate that one item does not rely on another.

FAQs

How is "independently distributed" used in statistical modeling?

In statistical modeling, "independently distributed" is used to describe variables that do not influence each other. Assuming variables are independently distributed simplifies calculations and allows for the use of specific statistical methods. However, this assumption must be validated to ensure the model's accuracy.

What does it mean for random variables to be "independently distributed"?

For random variables, being "independently distributed" means that the probability distribution of one variable does not affect the probability distribution of another. This is a key assumption in many statistical tests and models, like those involving "identically distributed" variables.

What are some alternatives to "independently distributed"?

Depending on the context, you can use alternatives like "statistically independent", "uncorrelated", or simply state that the variables are "not correlated". The best choice depends on the specific nuance you want to convey.

Is there a difference between "independently distributed" and "identically distributed"?

"Independently distributed" means that the variables do not influence each other. "Identically distributed" means they follow the same probability distribution. Variables can be identically distributed without being independent, and vice versa. Often, in statistics, we work with variables that are "identically and independently distributed" (i.i.d.).