All Questions
Tagged with quantiles normal-distribution
82 questions
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Integral of Normal and Poisson Process
I'm trying to find the percentile function of a random variable
$$Y=e^{-at+b_1\sqrt{t}Z+N_t(\mu+\sigma^2Z)}+\int_0^te^{a\cdot s+b\cdot \sqrt{t-s}Z+(N_t-N_s-1)\cdot[c+g\cdot Z]}ds, $$
where $a, b_1, \...
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12
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How to determine the percentile with a certain confidence? [duplicate]
The so called characteristic strength of a material should be the lower 5 % percentile of the population, according to the Eurocode when verifying the load bearing capacity of construction works. The ...
7
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2
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866
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How can I reconstruct a normal distribution from a set of percentiles?
I have the 3rd, 10th, 50th, 90th, and 97th percentile values of a normally distributed variable, and I wish to generate a dataset that will allow me to query for other percentile values (say, the 67th....
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1
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273
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Bivariate normal covering circles and ellipses
I am looking at covering circles for cartesian coordinates given by independent bivariate random variables $X, Y \sim N(0, \sigma)$.
The radius of a circle that will cover proportion p of these ...
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1
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143
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Calculating the mean and sd of a lognormal distribution from the log mean and log 5th percentile [duplicate]
I have a mean and 5th percentile value from river flow data that are assumed to follow a log-normal distribution. From these, I need to calculate the the mean and SD of the underlying normal ...
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286
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Understanding usage of quantile function (norm.ppf), passing p vs 1-p
I was given a question related to the quantile function using scipy.stats.norm.ppf, along with its solution - which I don't understand.
I'm changing the question ...
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1
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How can I find the value $Q$ for which the given region is a confidence region for $\mu$ with confidence level $1-\alpha$?
Let $X_{11},...,X_{1n}\sim \mathcal{N}(\mu_1,\sigma^2)$ and $X_{21},...,X_{2n}\sim \mathcal{n}(\mu_2,\sigma^2)$ be iid distributed and such that $\{X_{i1}\}$ are independent from $\{X_{i2}\}$ and $\...
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1
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71
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Can I reasonably estimate the population mean and standard deviation from a large sample all taken at a single percentile?
I am currently looking at a dataset of Fair Market Rents which are determined at different percentiles over the years - for example, nationally in 1983 they were all set at the 40th percentile, and in ...
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45
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Best practice for estimating values between 5% and 95% CIs for multimodal distribution
How can I improve my quantile estimation method for estimating values between the 5% and 95% confidence intervals for a multimodal distribution (as a mixture of gaussians) ? Where the CI are only for ...
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2k
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Different Calculation Methods for Theoretical Quantiles of Q-Q Plot
There seem to be at least two different methods to calculate the theoretical quantiles in a Q-Q plot. In the following, the normal distribution is assumed to be the theoretical distribution.
Split ...
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4
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1
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447
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Estimating a quantile from an unknown distribution
I have a variable $x \sim N(0,1)$, of dimension $p$, with each $x_i$ independent. I want to find the quantile, $q$, such that
$$\mathbb{P}\left(\frac{\sum_{i=1}^p (|x_i| - b_i) }{c} \geq q \right) = a,...
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33
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How to interpret a point in the qq plot? [duplicate]
I am trying to understand the Q–Q plot.
Suppose I create a sample according a exponential distribution
...
- 256
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0
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898
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What determines y-axis scaling on a normal probability plot?
I've been investigating Q-Q plots, specifically the normal probability plot, to determine if a set of data I have is approximately normal. I.e., a plot of the data should be approximately a straight ...
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1
answer
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What does 0.5sigma mean?
I want to ask about a term about "this data is within 0.5 sigma". If I understand correctly the person first calculates standart deviation(sigma) of his data and multiples his/her std ...
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1
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61
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The simulated $((1-\alpha )\times 100)^{th}$ percentiles of the null distribution of a specific statistic [closed]
I've written this algorithm in R program:
as following
...
- 121
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28
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Self-study: Comparing Uniform and Normal CDF/quantiles for a given range
Not sure if the title is perfect. Nevertheless, there are two persons drawing $\alpha$. ‘A’ draws from $N(0,1)$ and ‘B’ from $U(-2\sqrt{2\pi}, 2\sqrt{2\pi})$. For which person is it more likely that ...
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About the Normal distribution
I'm having troubles understanding the following problem
Problem
The volume of daily transactions (in millions of shares) in the
New York Stock Exchange is a random variable that is distributed
...
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405
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Median ranks and percentile ranks
In Statistics by Freedman et al. there's this example
Suppose the percentile rank of one student on the SAT is $90\%$, among the first-year students. Predict his percentile rank on first-year GPA. ...
- 356
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0
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1k
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If I have 25th, 50th and 75th percentile, can I estimate 99th percentile?
Supposing I have only:
25th percentile: 0.56
50th percentile: 0.70
75th percentile: 1.10
I don’t know other data (sample size, mean etc. ). Only those three value.
And assuming data is normal ...
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329
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Possibilities for rolling two dice: one is six-sided and the other one is four-sided
I have seen a question from someone's old exam. Two dice, one has 6 sides and the other 4 sides. Question:
a) What is the probability that the possible outcome(sum
of two dice) would be at least 9?
...
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4
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1
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175
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How to find the Percentile of this distribution?
Let say, we have 2 IIDs $X, Y \sim N \left( 0, 1 \right) + \eta $
Now $\eta$ has a discrete distribution with values 0(-10) with probabilities 0.991 & 0.009 respectively.
Also assume that $Z = X+Y$...
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2
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461
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Best method of quantifying probability of new datum belonging to either of two distanced normal distributions?
I have two samples A and B from two separate normally distributed populations. The population mean of B is higher than that of A, but both are unknown. My aim is to find a threshold value between the ...
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1
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934
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Deriving Inverse of Cumulative Distribution function [closed]
let $f(x)$ be a probability distribution, and $g(x)$ be the cumulative distribution of that probability distribution (CDF)
By definition, CDF is:
$ g(x)=\int_{-\infty}^{x} f(x) dx $
Given $g(x)$, I ...
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1
answer
2k
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Difference between quantile and qnorm
What is the difference between the R-functions quantile and qnorm?
I have normal distributed data and want to calculate ...
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2
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1
answer
126
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Hypothesis test with simulated data
A simulation gave me the following density of data (grey histogram, blue kernel density estimation). Having an alternative input $I^*$ with the same distribution (green line), I would like to check ...
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0
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79
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Is it possible to get equivalences of Western Electric Rules in non normal distribution with percentile values?
I am not a statistician and I am a bit lost with these concepts, but I will try to explain my situation.
I have a non-normally distributed data, and I am trying to apply the Western Electric Rules to ...
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2
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10k
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How do I calculate the standard deviation of a normal distribution given the mean and a quantile value of that distribution?
How can I determine the standard deviation of a normal distribution with known mean and a known percentile value?
The known percentile value would be on the correct side of the mean (eg, for ...
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2k
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Quantile transform vs Power transformation to get normal distribution
I was introduced to the concept of quantile-based gaussian transform. To my understanding, it changes the value of the original data by each percentile to the matching percentile of gaussian ...
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Is it possible to calculate percentiles in skewed distribution without raw data (only mean, median, SD)?
If it is of any one's interest, the data is taken from the duration of men "last in bed" as studied here.
I want to calculate the percentiles (say, 95th) of a non-normal distribution without raw data....
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2
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229
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Normal Quantile Function With a lower bound not equal to infinity
I was recently at a statistics competition and a question came up as follows:
They drew a normal distribution with $\mu=7$ and the area between the values $7.75$ and $8.25$ equal to $0.12$. No other ...
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0
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209
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VaR/inverse cdf of transformation of normal variables
I have the following exercise to solve as good preparation for an exam:
NOTE: $VaR_p(X)$ = Value at risk = $F^{-1}_X(p)$
Consider the bivariate normal random vector $(X_1, X_2)$. The marginals are ...
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145
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Value at Risk VaR with monthly return
The picture below shows the problem. I have tried to solve in this way: 0,001*1,88+2400*0,002 by following a formula in theory slides. But obviously there is a problem in that. Could someone help me ? ...
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58
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Arbitrary manipulation of percentile given the mean and SD
Say I have math scores from a class of 50 students.
What I know is the mean midterm score is $50$, and the standard deviation is $30$.
So it is reasonable to assume that there is $50 * .16 = 8$ ...
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3
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5k
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Build a (normal?) distribution from $n$, quartiles and mean?
I have some data that is described by $n$, quartiles (+ additional quantile point) and the mean. Is it possible to rebuild or model this distribution from these statistics? As the median and the ...
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1
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78
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Confidence distribution for $\mu$ [closed]
Suppose that we have sample $x_{i}\sim N(\mu,\sigma^{2})\quad i=1,...,n$ and when $\sigma^{2}$ is known. A confidence distribution (CD) for $\mu$ can be written as follows (see, https://en.wikipedia....
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1
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558
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Statistical time series analysis using Percentile and Empirical Rule
I analysing time-series to see the range of an asset. I have data for GBPUSD so i could only analyze this so far.
I have used both empirical rule and percentile. Of course they give different ...
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1
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32
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Is there a most accurate statistical model or they are used for different distribution? [closed]
I know empirical rule and use it for a normal distribution data. I know percentile and i use it too and love it. But are there any other statistical models? Or what model gives the most accurate ...
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1
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2k
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The correct way to fit a normal distribution to truncated/trimmed data
I have data where I believe that most of it is normally distributed, but a few extreme outliers are drawn from a different distribution. To estimate the mean and variance of the normal part of my ...
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1
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1
answer
127
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What can we do given percentile values of the data? [closed]
We are given 20 percentile values say equally spaced percentiles 0 to 100 and also the sample size. Basic things we could do is figure out if this is normal using qq plot, other than that what else ...
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How is quantile estimator constructed?
It is a popular practice to check if the random sample comes from a specific probability distribution by plotting a quantile-quantile figure.
For a finite sample one can only use an estimator of a ...
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2
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78
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Quantiles of normal distribution transformed
Let $Y_1 \sim N(2,1)$ and $Y_2 \sim N(5,(\frac{1}{2})^2)$. Let $X = Y_1+Y_2$. The mean and variance of $X$ can easily be computed to 7 and $1/4+1$. How do I determine the quantiles?
$Y_1$ and $Y_2$ ...
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1
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206
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Convert values between two normal distributions [closed]
Imagine, for example, I have two normal distributions of scaled scores:
...
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0
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11k
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How to calculate percentiles given standard deviation, mean and normality [duplicate]
I apologize if this question is exceedingly simple, but I did not find the answer here on Cross Validated or on https://en.wikipedia.org/wiki/Percentile or on https://en.wikipedia.org/wiki/68%E2%80%...
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88
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QQ Plot Interpretaion [duplicate]
I have a daily time series and when trying to check for normality I am getting the QQ plot below. Any ideas as to what is the plot saying about my data?
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2
answers
1k
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Estimating the distribution from percentile score, top 50 and curve
I'm trying to estimate how many people participated in a game competition and what my percentile score is based on some public data provided by the host.
The data I have is:
Top 50 leaderboard (Let'...
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1
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1
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9k
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Basic Percentiles from Z Table and Vice-Versa
So I know this may be basic but I'm having trouble piecing together the right formulas and logic to understand this. Most of the Z-tables online seem to have different information than the one ...
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3
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4k
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Approximate variance for 99.5th percentile for normal distribution
My question is similar to this one:
Approximate order statistics for normal random variables
I am looking to find a formula for the variability of an arbitrary percentile of a normal distribution. ...
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1
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383
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Quantiles in mixture distributions - mathematical explanation
On R, I have created a mixture distribution via a convex combination of a standard normal distribution, and a normal distribution with mean -3, variance 1 (i.e. subtracting 3 from a standard normal ...
1
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0
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160
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Estimating a tail probability based on the sample mean and standard deviation
I want to know if a sub-population has the same upper quantile as a parent population. Assume that in the parent population, proportion $1-\alpha$ of the data lies below threshold $k$. I can observe ...
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915
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Copula Behaviour : Gaussian vs Student T -Numerical Stability
I would like to get your opinion on the following topic:
I am comparing the behaviour of Gaussian and Student-t Copulas.
I employ the follwing procedure:
Simulate N=100,000 samples from a Student ...
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