Investig Clin Urol.  2016 Mar;57(2):119-128. 10.4111/icu.2016.57.2.119.

The mathematical formula of the intravaginal ejaculation latency time (IELT) distribution of lifelong premature ejaculation differs from the IELT distribution formula of men in the general male population

• Janssen PK
• Waldinger

• KMID: 2363134
• DOI: http://doi.org/10.4111/icu.2016.57.2.119

Abstract

PURPOSE
To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population.
MATERIALS AND METHODS
We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness.
RESULTS
The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population.
CONCLUSIONS
Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT.

Keyword

Goodness of Fit; Gumbel Max distribution; Intravaginal ejaculation latency time; Lognormal distribution; Premature ejaculation

MeSH Terms

Coitus/physiology
Data Interpretation, Statistical
Ejaculation/*physiology
Humans
Male
*Models, Biological
Premature Ejaculation/*physiopathology
Reference Values
Time Factors

Figure

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  Fig. 1 (A) IELT distribution of men in the general male population (Five Nation Study 2005) [4]. (B) IELT distribution of the IELT in men in the general male population (Five Nation Study 2009) [5]. (C) IELT distribution of Dutch Caucasian men with lifelong premature ejaculation (Study 1998) [2]. N, number; IELT, intravaginal ejaculation latency time; SD, standard deviation.

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  Fig. 2 The combined Log-normal Distribution of men in the general male population (Combination of IELT. Study 2005 and 2009 [45]). The form of this gamma-distribution is expressed by the mathematical formula, shown in this Figure. IELT, intravaginal ejaculation latency time.

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  Fig. 3 Mathematical Formula of the intravaginal ejaculation latency time (IELT) of the general Caucasian male population (x=IELT at x-axis; f(x)=relative density of IELT in general male population on y-axis).

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  Fig. 4 The Gumbel Max Distribution of the intravaginal ejaculation latency time (IELT) study in men with lifelong premature ejaculation [2]. The form of the gamma-distribution is expressed by the mathematical equation as shown in this Figure.

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  Fig. 5 Mathematical Formula of the intravaginal ejaculation latency time (IELT) in Dutch Caucasian males with lifelong premature ejaculation (x= IELT at x-axis; f(x)= relative density of IELT in men with lifelong premature ejaculation on y-axis).

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  Fig. 6 The Gumbel Max Distribution of the intravaginal ejaculation latency time (IELT) in men with lifelong premature ejaculation (PE) (red curve) in relation to the Lognormal Distribution of the IELT in men of the general male population (blue curve). In the general male population, 99% of men of the IELT distribution is represented after an IELT of 1 minute, whereas only 14.6% of men with lifelong PE is represented after an IELT of 1 minute [245].

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